Lets see, I have:
2 OMGs (same as OM20)
My original OM1 (not MD) I bought new in 1974. I no longer own it (I vaguely recall trading it in on the OM2S). I have 7 ZUIKO lenses, and one Tokina zoom, which came with a body I wanted.
Yep, I am addicted.
The only downside to the OM1s, is that they were designed for a mercury battery - I have purchased one of the adapters for each, so silver oxide cells work.
Regarding the OM10 - look instead for an OMG (OM20). They are newer then most of the OM10s and have the manual shutter speed built in, but share the same lighter body and very reasonable (used) cost. They aren't as rugged as the OM1, and you lose the MLU, interchangeable screens and some of the system camera attributes.
With the exception of some very early Olympus cameras (not in the OM system) and a short-lived and remarkably unsuccessful foray into autofocus (the OM77 and OM88) ALL OM series lenses fit all the OM bodies, and work equally well.
The flashes are good too - I have 1 T32, and two T20s.
Yep, I truly am addicted.