On older frames, with the larger 1" headtube, you can use the factory cup with a mix of 1 1/8" headset parts and loose ball with 1/8" balls. You will need to have a few headsets for parts though and a bit of trial and error. You can squeeze 1 1/8" cup in to the frame, but it will ruin the head tube.
The frame can be cold set to run a cassette hub, and you will also have to narrow the axle a bit to fit the smaller rear dropouts.
There are adapters made by Problem Solvers that will allow you to run a derailleur that doesn't have a hanger in back.
Any shop can order you an American to Euro bottom bracket, or you can run a BB that will convert from American to a JIS square taper. Otherwise a BMX crank with with a Profile adapter will allow you to also run a front derailleur with a double or triple. Chainline won't be a problem with BMX cranks though.
DON"T run canti/linear brakes on back. I don't care what anyone here says, the frame will flex really bad with those brakes. It was not designed for those load (unless you run a booster or brace the frame). If you run an internal hub, the drum is a great idea. Otherwise, disk mounts with a 160mm rotor can work with proper bracing on the frame.
Now here is the problem. Old frames were not used to having stiff parts on them or the stresses that modern parts provide. The headtube can "stretch" or flare if you run a long travel fork (and mess up the geometry REALLY bad). I have also flared out bottom brackets with stiff BMX cranks.
No matter what, I encourage a build because it's pure fun and I love the look of old school bikes with modern parts. But in the end, you will have a noodle of a bike that really isn't that safe.
If you want the look of an old school bike, with a MTB geometry, look for a 1999 Schwinn Panther or a 2002 Trek Clyde or the Van Dessel line. I have the Clyde and it's an awesome bike that has a cruiser look, but will actually perform. I'm still on the hunt for the elusive Panther though.