Don't get Ubuntu. Ubuntu shouldn't really be used on anything that you intend to game on so don't even bother.
For someone named hollywood I would assume that you are in the US. A person with common sense would assume naturally that the person who wants to buy something is located in the US. I guess you didn't...
You won't get much of a computer for $600, though. Assuming that a windows license will run about $100 and a used monitor might run you about $50, that leaves you with a little over $400 (I added the keyboard and mouse in there somewhere).
Sooo... you might be better off looking at used computers in your area. I'm sure if you searched around you could find a pretty decent package for under $600.
If you didn't put the pieces together yet I wouldn't recommend it because of your rather low budget. There really is no point in building a computer for $400 because it would be mostly last-gen hardware which isn't even worth doing.
If you could scrape together or save another $200 you would be much, much better off.
