I'm assuming you're currently using some kinda point-n-shoot cam?
Read up a bit on composition etc etc and try it on your point-n-shoot first. (Tip: 1/3 composition rule is actually not written in stone..but it helps).
If you like photography, you'll need to understand that you can get some good shots from your point-n-shoot as well.
I do not recommend going beyond your point-n-shoot until you figure out what you really like about photography. Especially if you have a tight budget.
Once you figure that out, it's generally between Canon or Nikon.
Canon entry level 500D
Nikon entry level D90 (replacement D7000 is having some pretty rave reviews)