Batfink,
Buying 2nd hand can be a pain as you've obviously discovered! Solid choice the Giant for that price. Oft suggested and oft decided upon with few complaints. Make sure you test the competitors in that price range at the shops if you can incase something else suits you better. Also make sure you get the sizing dead on. Don't rush this bit. Pick the bike shops brains and make sure you're happy with the fit and setup.
Should be able to get some other stuff chucked in too. Maybe a £25 helmet, a pair of cycling shorts, pump, puncture repair kit, multi tool or a lock. All of which you'll definately/probably need at some point.
Enjoy your riding and the rain!
Tom