You can buy a reasonable Dell for under £200 on their outlet site (sometimes much less - I have a Dell 2.4GHz Celeron with a gig of memory sitting under my desk that set me back £70 about a year ago, and it's happily been on 24/7 since). The really cheap ones aren't great for games as they use integrated graphics and have no AGP or PCI-E slot, but would do all you ask apart from Flight Sim, as I assume strategy games aren't that graphics intensive (may be wrong!). If you do want something a bit more powerful, then the higher-spec Dells come in easily under £400. Just watch and wait, and don't buy the first thing that comes along.
I have to add the caveat that i'm not really a Dell fan, because the components are a bit cheap and technical support generally doesn't, but at the outlet prices it's hard to go wrong.
As for spec, just about any processor would be fine these days unless you're really into high end gaming, but look for a gig of memory and 80Gb as a minimum hard disk. Monitors are all fine these days too IMHO, even the cheapest of 17" TFTs seem fine to me, just check for dead pixels if you get a chance.
edit: I should also add that the Mac Mini is really nice...
