What model is this Omega? (with pics, serial & case number)

Most likely the dial has been repainted, and the "Case number: 887" doesn't really make much sense in the context of an Omega reference number. So there's not much to go on. The serial number (which is from the movement) dates it to approximately 1960. If you want better information, you should post photos of the inside. But if you are considering buying this, my advice is just to forget about it and move on. The condition of dial and case is not what you want.

Upon closer inspection, I may have been too hasty in assuming it was a redial, I would need more photos (preferably straight on) to be sure. The overall presentation (and the awful over-processed photography on light background) just looked overly prepped to me, and since the dial seemed suspiciously clean (and some of the printing looked a little sketchy), I jumped to that conclusion without enough justification. I wouldn't be surprised if the seller is hiding some flaws. I do think that the case is quite badly over-polished, which would be a deal-breaker for me personally, and I'm also not a fan of pale yellow gold. But we all have different criteria. In any case, if you are seriously considering a budget of 2000 GBP, you can get a really nice piece, maybe even a jumbo with a desirable movement, so there no reason to settle.

There is no need to infer 18k gold from service documents, which can always be incorrect. It should be clearly indicated by a hallmark and/or a stamp inside the caseback.

Finally, I don't think we can help you decide whether to buy modern or vintage, it's night and day. You need to decide that first, and then start hunting.