Usually I'll tune cars that I actually use; I almost never have the full power parts equipped unless it's for a specific PP number.
Take the RX-7 Infiniti III I use - I put the suspension, transmission, clutch, LSD, and the stuff like that in - while only doing the Engine Tune and finding the right exhaust. (I think it's the Semi-Racing one in this case... sounds almost identical to the sound bytes for the rotaries in TXRD2.)
Generally speaking, the transmission is a MUST for me - I adjust it each time for each track to what I think feels the most natural for it. Almost all of the '60s and '70s cars need it (I'm looking at the American muscle cars...) to make them... decently fun to drive.