Congrats on your new purchase. Being your car is so original (and you probably want to keep it that way as much as possible), here is the route I would go if it were mine.

1963 was the year Mercedes made the change to front disc brakes on the W110 chassis: early year models were drum and late year were disc. So yours must be an early '63. This means the factory parts are out there that will bolt right on to your car to add the factory disc brakes. If you look on the engine, you will see a cover where the vacuum pump would bolt on, and I believe the cam is inside that the pump rides on (you would need to remove the cover to verify). So what you could do is check out the junk yards (which I've heard California has a bunch) for cars that have the power front discs and get the parts needed, or buy a salvage car and rob the parts from it. The main items you would need are the vacuum pump and lines, brake booster and master cylinder, and front spindle assemblies with the discs and calipers. You shouldn't need the A-arms as I think they are the same, but wouldn't hurt to get those too. Might also need the brake linkage at the pedal. If you get all these parts, then it should be pretty much a bolt-on job.

As for which cars will fit, all W110 cars from 1963 to 1968 will fit. W111 body parts should also fit as they share a lot of suspension parts. I highly recommend you get a free subscription to the official Mercedes-Benz parts catalog (EPC). There you can look up your specific car and get all the part numbers you need. Then there is a parts search feature where you can search using the part number and no vehicle model data to backward search as to which models the parts fit. If you do some research up front, you will know exactly what cars you need to look for to get the parts for your model.

EPC-net Online - Subscription Step 1 of 3

Good luck.