What are the most important characteristics of the graphic card?What should I consider when buying one?

It depends on what you are going to be using it for. Gaming? Resolution? Screen size?

The pixel shaders, the memory, the architecture, the speed, etc all play an important part. The drivers are a big issue as well, but we hope that AMD/nVidia is doing their job there.

First, define what your budget is as well as what your current setup is. If you have a weak setup then you won't be able to get the most out of more powerful cards. Also define what games you want to play and at what settings you would like to play them at. Then, since your on Tom's Hardware, look at the charts to compare them.

http://www.tomshardware.com/charts [...] ks,30.html

If youre serious about gaming, 512 mb of memory. DX10 or better. Make sure it has the connections you have or may want in the future DVI HDMI etc. This is just basics, theres alot more to it whwen it comes to performance

I wanna use it for gaming.
I can see characteristics of my current card in gpu-z but I dont know what they mean.
So can u just explain what does it mean and how much is immportant for gaming:
1.Memory size
2.GPU Clock
3.Memory clock
4.Bus width
5.Bandwidth
6.Shaders
7.Texture Fillrate

The most important characteristic of the graphic Card is that it works! If they dont you can not use the computer.

The most important characteristic differs from person to person. Some want the fastest, some its the price/performance ratio, some its only price. For me its price to performance. The HD4800 is around 150-200 depending on where you get it. The HD4850 is $150 at Best Buy now.

1Haplo

1.- The card's "RAM" -> bigger resolutions require more VRAM for textures.
2.- The graphical processor "speed" -> just like in CPUs 1Mhz from ATI is not the same from nVidia. The logic "the more the better" works in the same line of cards: 8800's, 9800's, GTX200's, HD4000's, etc... Or if they share the same architecture (the way they "do" things).
3.- The video card's RAM "speed" -> same logic: the faster the better among types. Different GDDR's have different ways of using that "speed": x1, x2, x4, etc. This alone ain't a hard decisive factor.
4.- The "wideness of the river" -> more bits imply more lanes between the GPU and the VRAM. This alone ain't a hard decisive factor.
5.- "How much water can go trough the river" -> the merge of points 3 and 4 into 1 single metric. This can be a significant point to purchase.
6.- Kinda hard to explain in short, but they are the way the card "paints", "shades" and "sizes" things basically. Lame explanation, but meh...
7.- Processed things the GPU can write in the memory of the card per second. Kinda like saying "done things per second" in the VRAM.

If someone can clear up a few things, it'll be much appreciated, lol.

Anywhoo, if you get too technical, you'll get a headache instead of a video card purchase decision, lol.

Esop!

EDIT: Spelling xP

Thx everybody!It helps a lot!