I think you should be able to find a decent Geneve within your budget, especially if you look at the 70s models. They are often available in good condition and pretty cheap
Otherwise, spend some time here and learn the ropes. For instance, go have a look in the "other brands" subforum, and I am sure that some options you've never considered will suddenly appear. For my part, I have taken a liking to vintage Tissots, starting out with two specimens I found in second hand stores, to now where I have to models both from the 40s:
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Okay, the first one is outside your budget, but the second isn't. And a lot of Tissots use movements very like those in vintage Omegas and with a finish of the same level - but a much, much lower price
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