I'll chime in.... but best I can do is make a few recommendations.
First I'll tell you you don't need cat 6 cabling, all IP PoE cameras are 10/100 devices, unless you have a specific need for cat 6 you can use cat5 cable...
Hardware-wise do you plan on using a DVR or a network server to run the monitoring software, have you looked at any monitoring software yet?
Cameras.....wow, so much to choose from but you'll want to stay away from bottom of the barrel budget cams, personally I'd recommend (if your building your own system) Trendnet and Hikvision cams, both companies make cams up and down the price range in many different configurations, all appear to be good solid products and in fact are the same cams (some models) with different branding and firmware, still hard to beat. You will want to steer clear of any type of wireless solution..I can go into the reasons if you need to know.
PoE switch, personally I like Netgear, if you planning a very big system I'd go with a managed switch, they are pricey but you get what you pay for, I use two, one a 24 port it is a ProSafe M4100, the other is a ProSafe FS728TLP which is also a 24 port switch but only has 12 PoE ports (I have 3 buildings that I'm covering and the hardware is split between two of them)
The thing you want to watch for in your switch is the "pool power" which is the total wattage that is available that is spread between the number of PoE ports you have, the larger the pool is the better off you are, typical PoE IP cameras pull less that 10w each but it adds up quick as you build the system adding zones and cameras.
Server...again it totally depends on what you want and your end goal, I built a server based on a AMD 6300 that not only runs my monitoring software (Zoneminder) but runs a web portal, it will eventually house a mail server and serve up a couple web sites, it basically is a Ubuntu LAMP server running V14.x I can give you more details on it if you want to go that direction.
But the server would totally depend on what your going to run as monitoring software so it's something you need to research. IP cameras don't really care as they are just another network device taking up a IP address on your network.
I also use a rack server, as for HDDs you will want to stay away from SSDs and concentrate on drives that are A/V rated (Like WD purple drives) or NAS rated drives (like WD red drives) your monitoring software will be running 24/7-365 so you will want a server that sips power but has drives that are rated for non-stop use, consumer drives like WD blacks, blues, greens will die quickly when used in this type of application. (BTW I'm just using WD as a example not necessarily recommending them as there are better and worse) Same would go for a SSD, I doubt the life would justify the cost in the capacities you will need...but that is just my opinion.
Software.... as I stated above I use Zoneminder which is a freeware Linux monitoring software, it is powerful but very spartan in appearance but it does the job nicely and is being actively worked on so there are periodic updates that add functionality, it's worth a look but does require a LAMP server to operate on.
There are a lot of monitoring software programs, it's better to just Google it and take a look at what you find....just be aware that some of the programs that say they are free put limits on the number of cameras or other features that the free version offers, some even charge you per camera after you go over their set amount. ..just better to research and ask questions.
When you say live feed you mean? all the cameras will have a live feed local view, if you mean outside your LAN then it gets dicey pretty quickly, if you have a static IP from your ISP it is doable but if not then your talking about using a 3rd party site for hosting which isn't something I'd recommend..
Live backup at off site server.....do you mean events?
Cost....depends on your perspective I'll break my system down for you....
Server, I probably have 6-$700 dollars invested in it with 5tb of storage
Switches, the big switch was $289 the smaller one was $200
Cameras, I currently have 18 cameras running (final will be somewhere between 22-26 total) (good IP cameras run between 90-125ea...you can spend a lot more if you want) but we'll just round it off and say $1800 in cameras
Software = free
Misc cable and associated stuff (RJ45's, good cable crimpers, cable tester, punch down panels, ect) probably another $400
So you can see from above I have a rather large system, it's pricey but I've spent that money over a couple years and it will probably be another year before I'm done, so I have $3300 invested so far and I figured that I will be over $4000 when finished (I really want a PTZ but just can't bring myself to spend that much on one camera), nothing is really cheap about doing this and it's not really something I would recommend unless you own your home and plan on staying there for a good long time. If you rent I'd recommend buying a cheap stand-alone system that uses a DVR.
If you own your home there are a couple things to consider one being that a good CCTV system should lower your insurance rates, it is a asset if you choose to sell your home and you want to leave it, and most likely your neighbors won't like the fact that you have cameras....can't answer why but they either think you are spying on them or your hiding something from the police, either way pay them no mind it's your property and when someone breaks into their house you will be the first one the cops come to see if your system captured any of it..lol
Don't know what else I can tell you, feel free to ask me anything I'll try to answer, I'm not the smartest on this stuff but I do know that works for me in my situation.
Good Luck, and check out the thread that @MichaelLindman linked above lots of good info is contained there.