Not the best advice I've seen...
Don't get a 5400rpm HDD. That's silly. Most games would be fine, but some still use the HDD to load textures and stuff. Not to mention your load times would be awful. You should arguably stretch to an SDD - I've never really rated them, but you can't deny the benefit of instant load times.
Stock cooling I wouldn't recommend, but you can probably get away with. Same goes for a case. But there are huge cooling and noise benefits from having better ones. This is where buying used stuff on the cheap gives amazing results for very little.
And the one thing you should never compromise on, the most important part of any PC... the PSU. It's not just a case of going for a high wattage, you need it to be a quality unit (e.g. Corsair / Seasonic etc). Don't go for the Tesco value one, because it will fail, and when it does, it can take the rest of your PC with it.
As for peripherals, a decent monitor is important, mouse too, but any cheap keyboard will do.