Hello there.
Firstly, your in the UK, so a couple of handy websites;
AmibenchPretty much the best place to find 2nd hand amiga bits for sale.
Also,
EyetechAre one of the best places to get new Amiga bits :-)
Okay then. As others have said, the easiest thing to do is buy a second hand laptop hardrive. These use a smaller, 2.5", IDE connector, whilst CD-ROM drives and ordinary PC hard drives use a larger 3.5" connector, which you can still use in your a1200, but you'll need an adpter, and probably to modify your case so that it'll fit :-) Finally ,you really want a hard drive thats 4gb or les, as the built in filesystem can't handle bigger drives, so you'd have to sort that out. You can always add a bigger harddrive later and copy over your install and ad a new FS.
EDIT: Damn, 2 people beat me to it! :-P
RIghty then. Next, as others have said, an accelerator. The built in CPU is to frank ,rubbish nowdays.
Amigas use Motorola processors numbered 680x0. the built in one is a 68020 with no maths processor. I'd recommend at least a board with a 68030 and an FPU (maths processor) and that it has or you get hold of at least 16mb RAM for the board. Although a 68040 with built in FPU would be better. Still at least 16mb RAM though.
For getting on the net, you need a PCMIA modem that works with the amiga.
The site mentioned above,
Aminetis the biggest source for amiga shareware, freeware, drivers, etc so i'd look there to see what cards work.
Oh, this isn't meant to put you off, but go to
Sabrina Onlineclick 'Archive' and look at the oldest comic going to see what your up against trying to get on the net ^_^ :-D
I'm sure it's easier than that lets on though, and there's people here to help as well :-)
Well, hopefully this will help a bit :-)