There are extremely few outright Omega fakes, so that is little to worry about.
You have to make up with yourself whether or not you'd mind a watch that has been restored (called a lot of things on eBay: restored/rejuveniated/refurbished. On here: "ruined") or polished to a shine, or perhaps repaired with incorrect, but functional, parts or if you want a 100% correct watch.
If you want a watch in the first category, no harm done - just don't expect your watch to hold/gain value.
If you want one in the last category, spend some time looking through the huge back catalogue here in this forum. Start here and work your way forward:
https://omegaforums.net/forums/vintage-omega-watches-help-discussion-and-advice.23/page-262
And welcome, by the way
Click to expand...