Sounds like a very nice deal! One tip though.. Open up the a2000 and check if the barrel battery has been removed. A big problem with these is that they tend to leak when they age, which in turn will make the acid kill the amiga over time.
The battery in the a2000 is only for keeping the clock while the machine is turned off. If you really need this, then you can get a new replacement battery for cheap.
And welcome to amiga.org :-)