Heya Becky,
Did you buy a third party graphics card or are you just using the on-board graphics that came with the computer? If you plug your video cable in near where your USB ports and keyboard/mouse ports are, then you are using on-board video. If you plug your video in near the bottom of the case where all the horizontal slots are, then you are using a third party video card.
As far as figuring out which graphics card will work well with what game, there are several factors to consider. Every game will have a certain amount of graphics memory listed as the requirement, but that is far too general to really know how well the game will run on your computer even if you far exceed the requirements.
It is always easy to figure out if you have the requirements to run a game, but near impossible to know exactly what kind of performance you will finally get.
A lot of it is really just trial and error. If you end up becoming a gamer hobbyist, then you will find yourself upgrading components somewhat frequently
A good way to get an idea is to pick what game you are interested in playing and search around to see if there are any reviews on it that shows what performance people get with their setups. If it is a popular game, there should be performance reviews out there. Here is a good article that gives you an idea of what I'm talking about -
3D Graphics Performance in Team Fortress 2
If you can post what game you are interested in and what video adapter you are using, I can try to get you an idea.
