Hi Filip,
… and welcome to OF.
I’m a Geneve fan and think your potential purchase looks fine.
Hopefully it’s got a very reliable 565 movement and you should check that out.
I have a preference for 565s (date) and 552s (no date) automatics, rather than the later 10** movements. Parts are readily available and the movements comparatively easy to service. For a £600 purchase, I’d expect to have evidence of a recent service and, if it hasn’t, have a look around on eBay or Chrono24, where these are frequently less expensive.
For servicing you would send it to a recommended local watchmaker, not Omega, and could expect to pay around £150 plus parts, postage and tax.
A stainless steel case is a good choice and looks in good condition.
The hands and dial are fine for a fifty+ year old watch.
The T on the dial indicates tritium was used for the luminosity.
That said, if that’s the watch you’ve fallen for I can’t see any good reason not to buy it. Let us know