What to consider when looking for an inexpensive video card for high resolution monitors?

I have a full HD 22" monitor with a 1920x1080 resolution. I would like to get a video card that can handle this kind of resolution, but I don't have much money.

Can you give me some advice?

Things to consider when choosing a video card are (in no particular order):

1. Your budget
2. The games you want to play
3. Your image quality requirements

The best way I've found to choose is to find a good card roundup that has benchmarks for the games I want to play at the resolution of my monitor. For example if you like to play Left 4 Dead 1 or Dirt 2 this anandtech roundup shows that the gts 450 will be playable even at maximum quality, but Bad Company 2 would be playable only by lowering the quality settings, so at that point it becomes personal preference.

I generally go by benchmarks of my games rather than just looking at the specifications, but as an overview:

• More powerful GPU lets you run at higher resolutions with better image quality.
• The memory of a card is mainly used for textures rather than frame buffer so more memory == better image quality rather than higher resolutions.
• That being said pretty much any card made in the last year can run at 1920x1080 if you set the quality settings low enough.