The purist route would be to take it to a Rolex warranty station, and pay a heckuva lot of money to have it restored. I notice the band is non original, so that's $400 right there. It's easy to pay more for restoration than the value of the watch. I have a similar manual-wind Oyster Precision, vintage 1960, that's worth about $750 with original bracelet. The savvier "two-stage" alternative might be as follows: 1. Take it to a good jeweler who is NOT affiliated with Rolex. Have them ultrasonically clean and lubricate the movement, do a light soak cleaning of the dial and hands, and reseal to 1 ATM. That should run $150 or so unless the movement is heavily rusted. 2. Fit a generic acrylic crystal. There is no need to insist on a Rolex crystal, since without a date the crystal will have no cyclops eye. You'll then have a functional, patinated "vintage look" Rolex Air King. Cost: another $40 or so. 3. That age of Air King takes a 19mm strap. Pick out a moderately priced stitched calf strap, making sure the clasp is silver-colored. Don't bother paying for croc or a Rolex buckle-- the idea is to keep costs down for now. You'll spend another $35. 4. Wear the watch for a few years. When you're feeling flush, contact one of the many Rolex customizers on the web, and you can gussy the watch up a roman numeral face, a gold bezel, hands, and crown, and a maybe a stainless and gold bracelet. At that point, the watch will be a part of your life, and you'll enjoy the enhancements more.
This is sage advice in my opinion. The stories of people sending watches to Rolex USA for simple restoration, and Rolex running up the bill and "demanding" that the watch be made honest are legendary. Still, it's a great watch, and if there's sentimental value to it and money is of no concern, Rolex does beautiful restoration work, and the value of the watch bill be less affected.