The cheapest thing you can get your hands on.
Nowadays, in terms of hardware power, any old x86 box will be powerful enough to be a web browsing / simple game playing machine for many years to come. Web pages can only consume so many cpu cycles...
In terms of hardware reliability, the pre-built vendors - HP, Dell, etc - are probably a better bet as they should have a warranty that covers the whole machine. If you built a machine up from bits and pieces, the warranty would only cover that single bit. However you will be paying a premium for buying a pre-built.