Vintage Omega watch help needed

You can get a nice vintage omega for that price, but it’s unlikely to be serviced and that’s going to be the issue.

Generally a vintage watch needs servicing every few years (between 3-10 depending who you ask).
A good service runs £200-700 depending on complications and parts required. The time required to service a £400 watch is generally the same as the time required to service a £20,000 watch so the servicing cost makes up a much greater proportion of the outlay on watches at the cheaper end of the spectrum.

If your budget is fixed at €400 I’d find the best Omega I could for that money, in running condition. Then save up for the next few months to get it serviced.

Don't just try to find the cheapest watch, decide on the watch you want and then try to find one for a fair price. For example, I'd avoid watches in plated cases and watches with damaged dials. Those will be cheap, but as @Davidt mentioned, it's not worth paying to service them.