I'd look for a rigid-fork MTB from the early 90s, when some of the really good names were still making top-quality off-road bikes with rigid forks.
Kona and similar. Lovely frame geometry, nice ride and you may be able to pick one up for chip money.
Unfortunately, cantilever brakes were in vogue at that time, so you get a six-dimensional chess game you can't win instead of a stopping system... but everything else is good news.
If you don't p[lan to use it off-road, you may want to dump the front mech, or at least lose the granny gear. Also, put some nice, sticky road tyres on it.
Even if you have to replace a lot of the gubbins, you'll still have a great frame.
I'm getting envious just typing this.