I've got a lot of Spohn Engineering parts on my 69, and I like the way it drives and handles.
A few tips in my opinion, depending on how much you want to spend:
Freshen up the front - that means ball joints, upper/lower control arm bushings, shocks, tie rod ends, steering link, idler arm, sway bar links --- basically everything that's rubber. I like polyurethane bushings on the front and I don't think my car is harsh or noisy at all (but then it's hard to hear much over the engine
Good shocks are a must.
If you want to spend more/upgrade more, look into good tubular control arms and perhaps even a coilover system - but get ready to spend some money.
At the rear - don't go with urethane bushings unless you're also replacing both upper and lower control arms with some that have fully articulated/spherical joints (in which case those joints will replace the bushings anyway). Reason: the design of those triangulated rear control arms make it so that in order for the rear axle to 'twist' in the car (like when the body rolls in a corner) something in those control arms has to twist. Normally that will be the rubber bushings. if you replace them with hard urethane, something is still going to have to twist and it might be the arms themselves, or the mounts --- and stuff is going to tend to break.
Again, good shocks at the rear are a must and either fresh rubber everywhere, or upgrade to control arms with spherical joints. My opinion is that there really is no middle ground between those two options. You can add a 70-style factory rear sway bar set up if you can find one, but it also requires boxed lower control arms for the mounting bolts. Spohn also makes a rear sway bar that anchors to the frame (as it should) instead of to the control arms. That's what I'm running on my 69.
Another good add on is to install rear control arm mounting point braces to help control that twisting tendency I wrote about above, and also on cars that are carrying some power and can hook.
UMI is good. I'm running their control arm braces. As I mentioned I like Spohn also. Those are the only two companies I have first hand experience with, but I know there are others out there who make good stuff. QA1 comes to mind for their coilover systems and shocks.
The least expensive route is going to be just freshening up everything with factory parts and good shocks. You'll be surprised at how much difference that will make.