'64bit'...only if you are using a large network.; It will make no difference on home computers.
'play some games'...unless you are seriously into gaming most current computers will be OK.
I would go for a Medion (£749 w/o monitor from PCW...256mb graphics, 512mb RAM, DVD/CD writer, more useful programmes than you can shake the proverbial stick at, 160GB HD, excellent media centre...TV...radio...DVD etc., etc.) Unless you are a mad gamer there should be little need to upgrade for yonks.