Rolex Oyster Perpetual Datejust Questions

Based on the recess of the dial (aka "pie-pan" shape) around the outer edge, that appears to be a ref 1603 with a lovely and interesting dial. I assume that there is no quick-set date (i.e. you can only change the date by moving the hands through 12 midnight). The bezel is known as "engine turned", but it has lost it sharpness through polishing, which is a bit strange, people don't usually try to polish those bezels. If it were my watch, I might consider replacing that bezel with a period-correct bezel in better condition, but that's purely a cosmetic issue for personal taste. Most likely the watch is from the 1970s, but if you remove the bracelet and take photos of the numbers between the lugs on both sides of the watch, you will be certain of the reference number and serial number, which will help you estimate the production date. There may be other useful information inside the case-back, if you ever have it opened up. The bracelet is a later replacement jubilee with solid links, but it's also pretty loose at this point. There would be no harm in replacing it with a tighter one, since it's not original anyway.

If this were my watch, I would be inclined to send the watch to an independent watchmaker who is experienced with vintage pieces. Rolex might want to replace some parts that you would prefer to preserve, particular the hands and dial.

P.S. My condolences on the loss of your step-father. It's wonderful that you have this excellent heirloom as a tangible remembrance.

If the dial is completely flat all the way to the outer rim, as @Nla91 suggests, then it will be a 16030 instead of a 1603. In that case, the crown should also have three positions once you unscrew it, one for winding, one for setting the time, and one for setting the date. The movement for the earlier 1603 had only two positions, winding and time-setting ... no quick-set date. I personally love the older pie-pan dials, but I have to admit that the quick-set date is a major upgrade in convenience.

Regarding the bezel, I wasn't urging you to change it out. Really I just wanted to mention that if you chose to do so, it wouldn't devalue the watch if you found a suitable replacement. As you can see from the photo you posted, the texture of the bezel has lost its sharpness.

There is an excellent person for vintage Rolex in the Dallas area. Bob Ridley can do whatever you want, and will take good care of the watch.
http://www.watchmakers.com/www/servicesRolex.html

Then it is going to be a ref 16030 as you suggested, likely from the 1980s. Again, the reference number (16030) will be between the 12 o'clock lugs, and the serial number will be between the 6 o'clock lugs. The latter can be used to get an estimate of the production date, within a year or two, using tabulated data easily found on the internet. With the drilled lugs, it's quite easy to remove the bracelet.

Nice watch and a great gift to remember him by. I have been hunting for a 1603 (birth year) for some time and I have seen the bezels polished like this
more often than not sadly. If you look at the profile pic you showed, you can see how a former jeweler/watchmaker ran the watch across a buffing wheel and the brushing on the case is more pronounced in the mm or two between the bezel and the lugs.
I love the way a sharp engine turned bezel plays the light and agree with Dan that there would be no harm in sourcing another bezel, your watchmaker can eaily replace it and you can save the original- entirely up to your taste though.