You should have no problems doing everything you want to do with a bog standard basic laptop.

I recently purchased a Toshiba c855 laptop from argos's ebay outlet for £280, And that came with a 1tb hard drive, 8gb ram and a pentium b960 CPU which is more than adequate so you should have no problems getting something in that price range. Off course my laptop was a refurb from the outlet but it still comes with guarantee's and warrantys. I'd normally stay away from the likes of pc world or currys as generally I feel they have inflated prices but if you go instore and have a look you may see an older model being sold a bit cheaper.

If that's genuinely all you are after pretty much any named laptop in Tesco/Asda/Sainsburys etc would suffice. I genuinely wouldn't worry about specs, just go into the store of your choice and buy the colour/design that takes your fancy within your budget. If it's a laptop on sale now by a brand you've heard of, it'll do all the things listed.

You don't need Windows 8 as you are unlikely to get a touchscreen laptop for that price yet, but it's not a problem if you do buy a Windows 8 non touchscreen as you are only one mouse click away from your normal desktop anyway. Steer away from netbooks (The small 10inch laptops) as they are unlikely to have a DVD drive.

Might be worth looking for dead stock new/unused laptops that run windows 7, I haven't used 8 much but when I have it hasn't been fun. Could get a bargain too for what you're looking for.

Don't forget that you will need either broadband (or a dongle) to use your laptop to access the internet at home.

What everyone else has said, but with the added advice that Windows 8 is a big, steaming dog turd of an OS that should be avoided like you would avoid a dinner party to which Janet Street-Porter was invited.