Alright, let's start with the resistance rating (ohms). The higher the resistance (measured in ohms), the less efficient the headphones are at moving the signal from the source (where you plug the headphone into) to the drivers (the pieces in the headphoens that move to make the sound waves). Most cheap headphones and pretty much all headphones meant for the masses are going to have a low amount of resistance, since most people don't have the hardware to smplify the signal enough to overcome the high resistance. That said, higher resistance can give headphones a different sound. The link below will explain the difference between the different ohm versions of the Beyerdynamic headphones.
Now, the difference between a DAC and a sound card. They essentially do the same job, which is turning the data that music is stored on the computer as into a signal that can be used by headphones. With cheaper products, this won't be much of a concern, but technically, a DAC only decodes the data it is sent and is completely incapable of changing the volume. You need an amp of some sort for that. Like I was saying though, that won't be too much of a worry at the lower end of the price spectrum as the DACs will come with amps built in so that it is an all in one unit. Technically, sound cards have both a DAC and an amp inside of them (if I'm not mistaken). The Fiio E10 that was linked above also has both a DAC and an amp. They perform the same job. Here is the difference, sound cards are aimed at the masses and computer enthusiasts who want something for their expansion slot which will give them better sound than the integrated audio which comes on the mobo. DACs are aimed at audiophiles. They don't much care about the convinience of having it built in to the computer, they just care about audio quality. If you want good sound, I advise getting a DAC/amp. The E10 is a good and cheap choice. It is capable of pushing most headphones barring the ones with higher resistance (I would say that an E10 would be fine with the lion's share of headphones, except something with like 600 ohms, but I don't know FOR SURE).
Back to the headphone reccomendations. Seeing as how this is your first venture into the audiophile world, I would advise against getting the AD700. They are known for their open sound, detailed nature, and being incredibly bass light. That makes them fantastic for listening to classical music (depending on your tastes) and for competative foot-step-listening (think first person shooters). They are great headphones for what they are, but I doubt that they are what you want. The M50 is a very good all around headphones, but there are better headphones to be had around the same price, so I wouldn't advise getting those. The RP-HTF600-S is another headphone that is great for what it is. It has a very fun sound that will please the masses. But seeing as how you are looking at spending a decent amount of money, and are looking into getting a DAC, I would advise against getting a cheap pair (they sound great for what they are cost, but much better can be had with the money you are looking to spend). The AD500 and the RX900 I don't know much about, however I know a good bit about the AD700 and the RX700. Seeing as how those headphones are in the same lines as the ones I know, I don't think I would reccomend either of those. I would expect the AD500 to be bass light like the AD700. The RX700 is a good budget can, so I would expect the RX900 to be pretty good for the price, but I think that better can be had.
An upper limit on your budget would really help, but I will throw out some general reccomendations. I do reccomend that you get something like the E10 or a decent soundcard (you would probably get better sound for the money with an external DAC). Better solutions can be had, but it is a really good option for a budding audiophile. However, if you would like to spend more on a DAC and amp, just let me know and I can throw out some reccomendations. As far as headphones go, I really don't like a loud and intrusive bass (ESPECIALLY when listening to metal. It makes everything sound confused and muddled). So bare in mind that my reccomendations will be based off of that (detailed sound with a tamed bass). Also note that I won't send you to a website that I wouldn't personally trust (I've used mp4nation myself and the audio forum I posted below is my favorite one so far).
On to the headphone reccomendations. The first thing that crossed my mind was the HM5 (http://www.mp4nation.net/brainwavz-hm5-studio-monitor-headphones). Good and accurate sound at a very reasonable price (considering what you get in terms of audio quality).
The Beyer DT990 Pro 250 ohm is currently on sale at amazon and I think it is a great deal. Look to the link below to get a desciption of how they sound to see if that tickles your fancy, but they probably won't be on sale for very long, so if you want them, move quickly. Do note that this will probably require some sort of amplification to get decent results due to their high resistance, so if you got these, you should definitely also get some sort of amp to go with them (I think an E10 would suffice). I advise getting something like the E10 anyway, but especially so with these headphones. http://www.amazon.com/Beyerdynamic-AMS-DT-990-Pro-250-Professional-Acoustically-Applications/dp/B0011UB9CQ/ref=pd_sim_e_79
The same goes for the DT880 pro as went for the DT990 pro. These should be great for metal if you are ok with spending this much. http://www.amazon.com/Beyerdynamic-DT-880-Pro-Headphones-250/dp/B001B1QENY/ref=pd_sim_MI_32
These are also a good option from what I've read about them if I remember correctly (check head-fi to see what people say about them if you are interested in this pair). http://www.amazon.com/Sony-MDRMA900-Over-Style-Headphones/dp/B007DCCK60/ref=pd_sxp_grid_i_0_2
If you want to spend a bit less money and don't care too much about build quality, this should be a great pair. http://www.amazon.com/Superlux-HD-681-Professional-Monitor-Headphones/dp/B00BWUHJFQ/ref=pd_sim_sbs_e_9
On the other end of the price spectrum, we have the HE400. http://www.amazon.com/HiFiMAN-HE-400-Planar-Efficiency-Headphones/dp/B007ZG32I4/ref=sr_1_1?s=electronics&ie=UTF8&qid=1375309101&sr=1-1&keywords=he400
As well as the Mad Dogs. https://www.mrspeakers.com/MrSpeakers-Mad-Dog-Fostex-T50RP-Headphones/MrSpeakers-Mad-Dog-Alpha-Pad-Fostex-T50RP-headphone
Both of those more expensive headphones will require a good bit of power and might need a bit more than an E10 can give. Something like a Fiio E17 would probably work decently though (there are plenty of better options for more money).
If you need me to clarify anything, or have more questions, feel free to ask.