The packard bell you're talking about has integrated graphics (not a proper graphics card) so it's unlikely to be that good for games.
This computer would keep you in business for years:
http://tinyurl.com/q63ojq
It has a separate graphics card with over 1GB memory, the processor is much faster, it has twice as much RAM and the hard disk drive is enormous!!
It's also got a TV tuner, so you could in theory record all your TV proggies on it with the humungous hard drive. And lots of other things besides.
12 months warranty.
It doesn't come with monitor though - but if you have one already you could use that, or shop around for a good one.
Many people make the mistake of buying what appears to be cheap only to find a year down the line, they are finding it's not good enough or new games won't play.
This one you might pay more initially, but it will last you a lot longer