Given your criteria, I agree with
@Fialetti's suggestion. The 600-series is manual winding, from the time period you are interested in, and in your price range. If I recall correctly, they are often 34-35mm, which also seems right for you. These would also be relatively easy to find, authenticate, and service/maintain.
Older military watches would be a possibility, but that is a whole different can of worms, and can often require more research and education if you want to find something authentic. Not to mention that older watches can be more difficult and expensive to repair/restore. This is just my experience with non-Omega military watches, so perhaps it is not representative.
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