The graphics card, or video card, is one of the most important aspects of your gaming computer's setup. In most games, it will be the botteneck for performance, and a good GPU can completely change your experience. They are also critical for some other tasks like modeling and design.
In general, the best way to categorize graphics cards is by their power. More expensive cards deliver higher speed and better performance with more details enabled. This performance, in turn, is easiest to rank using screen resolution. This is because higher resolution means more screen space that has to act as the display, so higher resolution makes the card work harder. The top shelf of GPUs should be able to run a modern game at full quality settings in 4K, which is the highest resolution available. 4K requires a special monitor and as yet there is not much content available for the format, but it is a worthwhile benchmark to denote the most powerful cards. These are the industry leaders in performance, although they may feel overpriced in comparison to cards in the lower tiers. You will pay a lot for the best, but these cards are also the most future-proof because they stay relevant the longest.
The 2650x1440 resolution is the second-highest typical resolution for desktops. It is common in high-end setups because more games can take advantage of it, making it more practical. This resolution is often branded as "QHD", which means Quad HD. The "Quad" part of the name refers to the fact that this resolution is four times greater than 720p, which is the classic HD standard. The cards at this level are the ones just below the top tier. There is a corresponding falloff in prices, making them good value buys while still delivering excellent performance. Individual games vary, but these cards should be able to handle maximum settings at QHD resolution, or at least make the game playable.
1920x1080 is called "FHD" for "Full HD." This standard became popular a few years ago as the second wave of HD quality. It is common in many midrange monitors as well as televisions. Sometimes shortened to 1080p, 1920x1080 is enough for great visuals, but the cards in this range are more affordable. You can treat this as the lowest tier for dedicated gaming setups. Its popularity means that people who have not recently bought a new monitor are likely to have it, giving it a large potential market.
The first HD standard for screen resolution was 720p. 720p is most common today among older monitors and setups where the owner has not bought a gaming monitor. You should consider this entry level. For example, if you have an older monitor and have never bought gaming hardware before, getting a graphics card in this range can get you a huge performance boost at a relatively low cost in money and effort. 720p and its close cousins are also common in laptops, but it is generally prohibitively difficult or impossible to upgrade the graphics card in a laptop.
The two major card manufacturers, AMD and Nvidia, produce a large and confusing array of products, often having similar names and undergoing multiple revisions. Do careful research to make sure you are buying the product you want.
Particularly at the advanced end of the spectrum, gaming setups require power sources, cooling, and other special support hardware. Your graphics card needs to both physically fit inside the case among these elements and interface with them properly, especially the motherboard.
Think carefully about how much you are willing to pay and how much performance you really need. Any card will eventually become obsolete, so don't pay too much for something you will need to replace within a few years.
The best possible performance comes from operating two top-end cards from the same manufacturer in tandem, which is called SLI mode in Nvidia chips and Crossfire for AMD. This double-card setup is better than any one card, but currently there are not many motherboards that support it, and it is expensive.
Many cards generate a lot of heat, which means you will need to buy a cooling system if you do not have one already. Not all cooling systems work with all cards, and vice versa.
The two biggest and most important brands are associated with the two largest manufacturers, Nvidia and AMD. They tend to release new cards at the same time and at any given time, one company or the other might have a card that dominates a particular category. This is particularly complex because card prices change often, especially in the weeks before and after a new product arrives on the market.
In general, the current best card from Nvidia is the GeForce GTX 980 Ti, and the top AMD card is the Radeon R9 Fury X. However, both companies have new top cards arriving very soon.
The best second tier cards are the Radeon R9 390X from AMD and Nvidia's GeForce GTX 980. Note that very small differences in model designations might involve very different cards.
The third tier, 1080p or FHD, includes many cards at a variety of price points. At the top end, Nvdia's GeForce GTX 970 competes with the Radeon R9 390, while among cheaper cards, you'll see the GeForce GTX 950 2GB against the Radeon R7 370s 2GB