I think Neil has posted some good pointers, £300 should definitely get you a good spec steel bike, look out for Reynolds or Columbus frame tubing, forged drop outs and a built in gear hanger. Generally, £300 should get you a better complete bike than it will a frame and parts to build. Build projects can easily run away cost wise.
A lot of bikes will be sized in inches, so I'd say you're looking at 21" / 22" frame. Look out for the 'stand over height', with a 30" inside leg you'd want a stand over about 29.5". Not everyone lists it, but its a good ball park for fit rather than you're height. Two 5' 10" people can have completely different leg and back lengths.
Name wise the list is endless, but sticking to the above should eliminate most of the crap