The OM-1, -2,-3, and -4 were Olympus' top of the line cameras.
The OM-10 is an auto-exposure-only camera (you set the aperture and the
camera sets the shutter speed) unless an optional manual adapter is
attached allowing manual shutter speed settings. It's not a very robust
camera -- make sure it is working before buying one.
The OM-1 is a nice camera but it uses a mercury battery that is
technically not available anymore in the USA. There are equivalent
batteries available but they do present other minor problems that you may
not want to mess with.
The OM-2 series models (OM-2, OM-2N, OM-2S) use easily available
batteries and they are fine cameras.
The OM-3 and -4 series cameras command higher prices due to build
quality and metering options. They are very, very nice.
Other models that would probably suit you are the OM-PC (aka OM-40)
and the OM-2000.
Light seals are foam strips that surround the cameras film chamber and
make it "light-tight" (so the dark doesn't leak out

)
On Japanese cameras made in the 60s-80s, this foam material can
degrade and requires replacement. Whenever shopping for a vintage
Japanese film camera ask about the film seals before buying unless you
want to replace them yourself (it's not very difficult).
As with any used film camera, make sure it is in good condition before
buying. Either buy from a reputable eBay seller or from a dealer such
as KEH.
If you want an inexpensive, recently made Olympus-mount camera
that shouldn't have problems with seals, I would recommend the Olympus
OM-2000. It was made from 1997 up until fairly recently and is a good
basic camera.
BTW, in order to use OM lenses on your e620 you will need an appropriate
adapter. But, it's also true that you can use many lenses with different
mounts on your e620 as long as you have the correct adapter. So, you
don't have to only consider an Olympus film camera.