Game time loading typically doesn't improve (but it can, in some cases). Frame rate, however, will increase dramatically with a better card (since it can process more things more quickly).
The advantage in graphic quality does not come so much from the card, but from the fact that you can pick higher level options in the software and still have reasonable frame-rates. You can think of a graphics card as a seperate computer that does nothing but graphics. So, getting a better one is like getting a new computer. The new computer can do the same things the old one can do (and a few extra things), but it can do them a whole lot better.
So, things you'd look for are clock speed (which is exactly the same concept as your CPU speed), memory (just like RAM), memory type (DDR, DDR2, DDR3, DDR4), and interface with the computer. Interface times are mostly going to be based on what kind of slot it plugs into (AGP, PCI, PCI-E). With all of those, there are different rates the computer can talk to the card (both from width and bandwidth). If you go from PCI to a PCI-E x16 that uses the full PCI-E x16 bandwidth, it'd be a lot like going from dial-up to a T1 connection (not numerically, but it'd feel something like that). Because game loading sometimes comes down to how much graphics information is ready, this can increase speed a bit. Your motherboard and CPU will still influence that, though.
It's all a balancing act, if you dont' have lots of money to spend on a top-end card. You can get faster cards that have less RAM. You can get cards with less RAM that is better (DDR4, rather than DDR3, for example). Then there are drivers, which can be better or worse depending on manufacturer and card.
I've always been partial to ATI, but that's partly because I go for mid-range cards. In my experience, nVidia is great at the high end, but falls off for those of us on a budget. Some people disagree with me. The driver support from both companies is interesting and seems to depend on what year it is.
If you start looking at dual cards, you need to know a lot more about your computer. For instance, can your motherboard support that multi-GPU setup? For nVidia, you have to have an SLI compatible chipset. For ATI, you need Crossfire compatible. At that point, you also have to think about power requirements and make sure your computer PSU can handle it (see how expensive this could get?). The main advantage of 2-GPUs is that it's like going to a dual-core CPU. You can split tasks, which again improves speed.
Let me know if you need more info.
