In reply to TryfAndy:
Well done for taking it on yourself!
I agree with MHutch though. Full toolkits invariably have loads of stuff that you don't need - technologies advance quickly (e.g. the tool to extract a modern outboard bearing BB is very different to that required for older models such as octalink, ISIS or square-taper - all of which are different).
> The rear axle has started to disintegrate and make some less than attractive noises
For that you just need some cone-spanners and maybe a handy adjustable spanner. And patience.
> bottom bracket sounds like it's full of gravel and wobbles all over the place
That means a new BB bracket (modern internal BBs are cartridge-based, so not servicable) and a tool to remove/fit- check your new one is of the same type as the old one otherwise your cranks won't fit.
> hat and the fact that I need to do a full strip and overhaul anyway, with complete degrease, deep clean and re-lube, plus cable changes etc.
If your bike was made at any point in the last 15 years then all you really need for this is a decent set of allen keys, maybe a spanner or two. If you really want to a super deep clean then maybe a chain whip, cassette tool, and chain-tool (depending on chain type), but with some good degreaser, decent brushes, and a chain cleaner, this might not be necessary.
The Park Tools website has a loads of great info on taking your bike apart and putting it back together again. Good luck!