New Member, Old(er) Rolex, Common Question

[RRRolex1969]

Hello Rolex Owners and Experts!

I am delighted that I found this site. I joined just this morning, and I am hoping to learn more about my old watch, and Rolex watches in general.

Back in 1985 my brother-in-law gave this watch to me (photo attached) as a graduation (college) present. I wore it for a year or so, and then it went in a drawer, and it hasn't seen daylight for 2+ decades.

I recently re-discovered it, and I took it to a local watch shop/jeweler who cleaned it and replaced the old acrylic crystal (not original) and the crown and tube (I have the original parts). It keeps time perfectly, and I would love to know more about it. I know that the band is not original (china). I would also be interested in some suggestions for a replacement band.

Here is what I do know - this stainless Oyster Perpetual is definitely older than 1985. My brother in law was in his late 50s/early 60s when he gave it to me, so it could be from the 50s or 60s perhaps. It measured 1 5/16" diameter (~33 mm). On the side it reads 1003. It does not have any writing on the face at the 6 o'clock position. No "Swiss" or "Swiss Made"...nothing. It does not seem to have any of the glow in the dark material on the face (maybe on the hour and minute hands).

I am guessing it is an "entry level" Rolex, and I would love to know more about it. How old is it? Perhaps more importantly - is it authentic (I am thinking that the repair shop would have alerted me if not - but I guess you never know)...

Thank you in advance!