It is possible, but you really should first pause for a moment and consider a few things before proceeding further:
- What graphics card will you buy - Go to this wiki page, look which graphics cards are good and then do a search for what you can find in stores. If you're looking for the most efficient mining cards, you might not find them, so you should take that into account.
- Check whether your motherboard can support said graphics card (shoudln't be an issue in most cases), whether it will fit in your computer case (can be an issue if it is very small or crammed), and whether your power supply can handle it (which probably will be an issue with higher-end cards).
- Check whether mining is really the thing you want to be doing - the profit margins might not be too high at the moment. You can for example use my mining calculator - put in how much your graphics card and power supply will cost you, how much power the whole computer will consume, how fast you'll be hashing, and how much does electricity cost you. It might turn out that you'll be mining at a loss. Even if you are not in red, lower the price of Bitcoins a bit and see whether you are still profitable. Difficulty appears to be rising slowly and the price of Bitcoins can always go down, so you have to be mindful that what you can get at the moment might not be the same as what you can get in the future.
If everything appears to be in order for you, you can try going for it, otherwise you might want to consider just buying some Bitcoins at an exchange and hoping the price will rise. So all in all, it is possible to use your old hardware with a new graphics card to profitably mine Bitcoins, but you have to consider a few factors before making the decision.
As for a pool that is good for a small miner, basically any of them work. Compare them and pick whichever works best for you.