Help me pick an AP router

So I realized the Wireless connection in multiple parts of my house .... sucks to put it bluntly. So after discovering what a repeater and Access point was I set out to configure it within my own home.

Now I plan on doing this by running a power line from my Modem/Router to a secondary router upstairs that will function as an AP thus extending my connection without losing speed. The question I have is should I use this router as an AP or just a router what exactly is the difference since my modem and router are one?  

The second question: I have 3 routers to choose from and I needed advice as to which one to use.

Asus RT-N10+: http://www.asus.com/Networking/RTN10_B1_RTN10Plus_B1/

Linksys WRT110: http://support.linksys.com/en-us/support/routers/WRT110

Airlink 101 AP421W Super G™ :http://airlink101.com/products/ap421w.php

Which one of these would provide the best signal range without compromising on speed?

And finally Based off your answer to the first question would it benefit me at all to run custom firmware (DD-WRT, Open WRT, Etc) vs stock firmware?

Any other tips/advice is always welcome 

Imo the Linksys there looks to be the best of the three. I have an Asus N56U router, I like it, but I have problems with it from time to time because I can't find custom firmware for it.

and then should I run the powerline into a WAN port and use it as a router or into a LAN port and use it as an AP?

First off I'd say we more information. What kind of environment will this be in? Apartment? House? Office? How many clients will you have? What will you be using the wifi for? Movies, gaming, streaming, file sharing? How big of an area does it need to cover and are there multiple floors it needs to saturate with wifi?

The only one from the list you provided that supports dd-wrt/openwrt is the asus, you can check yourself by heading over to the DD-WRT Router Index. After you find an ap/router you like, I'd definately head over there to see if you can flash the firmware. I despise stock consumer firmware, and I think you'd appreciate the added functionality open firmware provides. You can read more about what it can do on their wiki.

None of these APs support the 5ghz band, I don't know what devices you are hooking up to this, but you are going to have a better experience on N-5ghz than you will on N/G-2.4ghz, especially if you are in an apartment or any kind of dense office/housing. Most modern devices support dual-band N, if I were you I'd spend the extra couple bucks to make sure your AP is equipped with dual-band as well. One easy way to tell is if it supports wireless-a, so when looking on newegg or something like that, look for a/b/g/n. That way you know it supports 5ghz-N, as well as 2.4ghz-N.

Your range and connectivity will only be as good as the environment you are putting this in. Companies can advertise their higher-than-standard-spec range all day long, but if you are putting this thing in a place with lots of metal, brick, electricity, etc, then there will be no way in hell you will get anywhere close to the advertised range. That range will ONLY work if it is in the middle of the day in the middle of an empty field with clear skies and absolutely nothing nearby. 

Also their advertised speed is poppycock. The moment you add any kind of security with WPA-TKIP the speed of that AP drops by at least 15%. Move up to WPA2-AES encryption and you are looking at most 1/3 of the advertised speed. But then if it's also a router, meaning it is also a DCHP server, NAT, DNS forwarder, the list goes on, it gets slowed down even further. So, the higher-spec the cpu and the more the ram, the faster it will be because then it can actually handle that crazy encryption. Likewise if it's just an AP and not a router.

So here's what I would use to compare APs with:

dd-wrt approved

Cpu clock speed

Ram

Dual-band or single-band

External antennas (so you can upgrade them with larger ones down the road if need be, increasing your passive gain and range, there are other advantages too)

Price

To see if I know what I'm talking about there's a list of my certifications on my profile page.

Hope this helps.

FIrst of all thank you for the comprehensive response ...This Wifi will be covering a house ... primarily rooms on the 2nd (I only have 2 floors) floor and a the living room that falls right below ( I have a very open concept house so the only physical barriers are those leading to the rooms (doors and walls) so my personal bedroom may have some metal support structures blocking signal in the wall but that is why the router will be placed in a corridor ... As for buying a new router I wasn't really considering it as I currently own all 3 of those and honestly I'm fine with a 2.4ghz band as all the devices connected to it (meaning 2 phones, 2 laptops, and occasionally a tablet) will only be using the internet for basic media consumption (occasional media streaming across my local network but primarily casual internet browsing/youtube/netflix streaming) .... as for External antennas I own a few to boost range ..... The Asus router spec wise (coudn't find the processor make) has more ram than the linksys and it supports dd wrt so I'm leaning towards that right now ... and finally my last question ... I'm not using this as a repeater because that effectively halves my speed but what difference would it make as to whether I used this as an AP or a router? I understand that an AP goes Modem -> router -> AP-> device but in my case the Base modem and router are one so what difference would it make if I ran the asus as a router vs AP ....

Also how much would the wavelengths of each device conflict with each-other? And I trust you know what your talking about ... therefore certs wont be necessary 

Alright awesome. Didn't read that part where you already had all 3 of them. Guess I could've shortened my response quite a bit xD

what difference would it make as to whether I used this as an AP or a router?

Very simply in router mode it will create a completely separate network, different ssid, subnet, everything. devices on this network will not be able to communicate with devices on the other network, and vice-verse.

In AP mode (which you can do very simply on stock firmware if you want) all devices connected can see everything and everyone on the network, and if set up correctly, devices can "hop" between other access points automatically based on signal speed and strength. This is the setup I have, 4 access points of various makes and models each with 2.4/5ghz N spread around the house, and they all communicate with each other both through the lan. I can be talking with a friend on hangouts in the attic and walk all the way to the basement and out to the backyard, hopping between all the APs, without losing a single packet. For security I added a guest ssid to each ap and turned on client isolation with ddwrt. So if someone comes over and wants hop on the wifi, I give them the passkey for the guest wifi, and once again they can wander around the house hopping between aps without losing a single packet. Way cool stuff. (if you're wondering I'm using tp-link 500mbps powerline adapters between them all)

So really it all just depends if you want devices connecting to this thing to be on a completely separate network or not. Also if you have more than 10 devices connecting to it at once it will be slowed down quite a bit more in router mode.

how much would the wavelengths of each device conflict with each-other?

Just make sure it's at least 3 channels away and you're good. In the States the general rule is to use channels 1, 5, 11 interchangeably (we can't legally use channels 12-14). If you have an andriod I'd go download wifi analyzer to see what channels are available. (my network is all on one channel, but that's because I also have a wds-mesh network set up as a backup link just in case powerline goes down)

If you want to set this up in ap mode on the same network it's very simple. Plug a cat5 into the lan port, set the ip to something on the same subnet, disable dhcp, set the wireless settings exactly like your main, just +/- 3 channels on the 2.4ghz spectrum.

Again Thanks a lot for all the input It's helped out quite a bit but I'm going to have to ask one last question ...

When "hopping" between different APs I know its obviously not noticeable for the avg. user but lets say I'm running a large file download on either my phone or laptop or any plethora of wireless devices and I walk upstairs and connect to the 2nd AP does the file download drop or do routers have a way of "handing off" the download so it continues without interruption. If they do have a way to seamlessly transfer is this a router specific dependant feature? In that some may have it and others may not or is it more of a software aspect?

Thanks again for all your help. 

It is exactly a handoff (that's actually the technical term). Most APs will do it automatically because it actually doesn't rely on the AP so much as the client. 

When the client finds another AP that it can access with a stronger signal, it will automatically send a disassociate/re-associate packet, and then bam, done. Now, let's say you are downloading your file, and you were just handed off to a different AP. Unless full mesh networking is set up, there will be a time, usually in milliseconds, seconds if the APs are overly burdened, that your download is paused. If those milliseconds are unacceptable, there are other options in mesh networking. (If you want to know more how the ap's know to continue your download, I think that's more an inbox question for wendell, I don't think I can explain it well)

To set up full wireless mesh networking, dd-wrt allows for OLSR, which allows allows your network equipment to talk to each other. The APs will then calculate the best routes for clients to take, and it will handoff clients accordingly. However, it assumes that you have 100% network reliability AND it assumes that there are additional routers in between subnets, and the way the dd-wrt wiki has you do it it assumes each AP is in router mode.

This is where WDS-Mesh comes in. WDS-mesh is similar to OLSR in that it communicates with other ap's for the best route for their clients, but is different in that by default it will act more like a wireless bridge, no need for a lan cable in between the two.

It's a good option if there's no way to send a lan cable out there, but I was out for speed when I set mine up, so I put in some scripts to fail over to WDS if the powerline goes down. My set up is a bit strange, I have 3 wireless networks, one main at 2.4/5, let's call it "bob-net," one guest at 2.4/5 "bob-net-guest," one hidden wds at 5 "bob-net-wds." During normal operation, wireless vlans keep the wds, main, and guest separate, that way I don't get a broadcast storm between the wds and lan segments, but if a powerline goes out, then wds automatically switches its vlan to link in with the main and guest, and switches its vlan link with the powerline network off. Then, every 30 minutes thereafter it will switch the vlans back to default operation. (hopefully that made sense I think wendell could explain this better lol)

If you are fine with a few millisecond pause between hops then something like a wds or olsr is not necessary, you can just set up your second router in AP mode like I said in the previous post and go, then handoffs will happen on their own.

That made sense Thanks again