What does it say on the top of the camera

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Does it say "MD" on the front left side of the body? If so, it is an OM1-MD. Otherwise, it is an OM1 (or the extremely rare M-1), and will only have the motor drive coupling on the base if it has been modified (and a fair number were modified).
As for the battery, a few years ago I purchased an adapter for about $30.00 that allows use of a G12 silver oxide cell instead. It works great, and can be transferred to other cameras.
I don't think it is an OM1n (wrong hotshoe adapter) but any of the alternatives (M1, OM1, OM1-MD or OM1n) are excellent cameras, depending on condition. Unless a CLA has been done recently, at the very least you will most likely have to replace the seals (common in almost all SLRs of this vintage). In particular, you have to be careful that the seals for the mirror haven't deteriorated badly, because the gunk can migrate into the pentaprism, and cause damage there.
If you have a local repair person you've used before, I would suggest asking them if they do CLAs on OM equipment, and what approximate costs are. If there is noone local, John Hermanson at
www.zuiko.com (who posts here regularly) is the goto resource.
There are a lot of OM1s around, so if there are apparent problems (like a missing or corroded self-timer lever) you might want to pass on this unless the price is very favourable.
Matt
PS by the looks of it, I would guess that the lens may be newer than the body.