Hi,
I rebuild bikes and manage on a set of 3 adjustable wrenches, a set of allen keys, some pliers, some needle nose pliers can be useful but not necessary. A hammer, a small diameter nail punch (this is for knocking out and reinserting pins on chains, along with a nut for the rear). Just make sure the third wrench is big enough for BB's and head tubes or use an adjustable grip. A socket set of reasonable quality is useful. I say reasonable quality as if the crank bolt is bigger than 14mm you will struggle to fit the bit in the gap with a cheap set. All cheap and readily available in decent quality. Second hand can probably have the lot for less than £30.
On top of this a parkers crank puller, about £10 new.
If you want to do wheels and hubs then as some have mentioned you need some more specialised tools like cone wrenches and kit for the spoke tensioning and wheel truing. if you want to fiddle with sprockets and remove them you will need a chain wrench. These things can be found quite economically though second hand.
Hope this helps.
