Probably 1950s , and around 33mm diameter in case size?
The dauphine hands were the style from that period, up till the early 1960s when many models switched the baton hands.
The Oyster Royal was once the top of the line rolex, but these days they are not terribly popular so not terribly expensive. You can find them in the range of $600-2000, depending on condition and completeness (box,papers). If inherited... priceless.
Get it serviced and keep it sell. Don't expect it to be very accurate though...not many old rolexs will be after so long, esp. if it was left worn and unworn intermittently for many years. I would also say the bracelet is probably rarer than the watch... so keep it on and keep it intact.
Can you remove the bracelet and look for the numbers on the case at 6 o clock and at 12 o clock ?.
That would help in finding the model and the year as well.
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