Sorry, I do not want to be the bi%ch of the bunch, but the better advice on the OP might be to give into consideration to NOT have the case polished, the dial touched and/or cleaned, but leave it as it is while it is functioning. Service of course to be conducted.
Please refrain from pushing towards your own preference (be my guest on your own watches), but give options to OP.
Best advice IMHO to the OP would be to have the watch assessed by a reliable watchmaker (not Omega) and read-up and learn on this forum, after (!) which one might decide on next steps. Especially if it is one's father's watch, take time to make up your mind (and do not haste yourself in cleaning, rubbing, polishing and all other activities that include the loss of originality).
Take your time, read-up and post some pics of the watch now and then: we like that
But that might only be My2Ksh
Edit: btw Diego: Welcome! And good to see you did some digging and research before posting!!
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