Which PC? Can it play Games?

those machines would struggle with anything other than flash games and older pc games. the processors are both excellent and the rest of the spec is good, but a better GPU is required. the asus would be good and just add a new GTX970 or radeon GPU and it would fly.

With that budget, you are going to struggle i think.

but prioritise the gpu first, something like a GTX750 isn't too expensive and will do a decent job for things like that.

Another option is to buy a pc without a gpu in and then get the gpu second hand, saving some money, an older generation second hand gpu like the GTX650/660 might be an option

for strategy games, i wouldn't go much lower than an i5, as these tends to need abit of cpu power to manage all the units and large maps.

if you are really struggling with the budget, then an AMD APU might be an option, they are generally better at games than the usual integrated graphics, and will beat some of the low-end budget gpus. It should do ok for the older games, but will struggle with more recent games

If you've got a mouse, keyboard and monitor, I'd suggest going for an AMD-based build instead of Intel. You could easily get a reasonably powerful PC that could do what you wanted for £500.

For example, something like a system consisting of:

AMD Piledriver FX 6300
Asus M5A97 Motherboard
1Tb Seagate Barracuda HDD
8Gb Avexir 1600Mhz DDR3 RAM
Sapphire AMD Radeon R9 285 Dual-X Graphics Card
Galaxy Evo Gaming Case
Corsair Builder Series 600W Power Supply

Come out at £503.81 at Overclockers.co.uk.

If you really needed an optical drive, then you could switch the R9 285 Dual X for a less powerful but still very good R9 280 graphics card that runs about £30 cheaper in order to add the optical drive.

If you're not confident about building PCs yourself, Overclockers do, I believe, ship systems prebuilt to spec if you phone them. Or you may have a friend who can do it?