Congratulations! Don't worry about getting addicted to cat sailing, after a while it will seem normal . It looks like you have picked up a very nice, ready-to-sail H16 for a very good price. That's the good news. The bad news is that to make this boat even minimally ready for racing, you are going to have to spend a bit more. Even so, getting into cat racing is relatively inexpensive and good racing is available at a skill and cost level with which you are comfortable.

Of immediate concern:
Hulls: From your picture, the hulls appear to be in really good shape. I would not go through the expense, labor and added weight of painting them. Instead buff out the oxidation with a random orbital buffer and buffing compound. Then seal the gel coat with Starbrite/Maguires-type boat polish. I think even your son (I'm assuming he's a teenager) will be impressed with the results.
Rigging: It seems likely that you have the original shrouds/forestay/bridle/trapeze(s). Replace all of these and upgrade to a double trapeze. Purchase (2) trapeze harnesses.
Righting system: Can be as simple or as complex as you wish.
Main blocks: The OE is a Seaway 5:1 system (2 single upper blocks and a double block over a ratchet block on the bottom). Replace with a 2.25 inch 6:1 system (triple on top, triple on the bottom).
Wind vane: A bridle mounted wind vane is vital, especially for downwind sailing. Also replace any telltales on the sails that have become frayed.
Rudder pins: Get a couple of sets of aluminum rudder pins. They wear quickly.

Recommended:
Batten caps: Get a complete set of the black batten caps for the jib and main. On the main, one cap goes on the inboard end and one (adjustable) on the outboard end. The OE white ones will crack and fall apart (if they havn't already).
Downhaul upgrade: Add the little plastic bearings for the gooseneck and a block for the downhaul.
Beach wheels: Roleez or Cat Trax. Saves your back and the bottom of your hulls.
Tramp: Examine the tramp carefully. UV will degrade the vinyl. To be class legal, a new tramp must be from Hobie. Lace the tramp as tight as possible as this is critical for a stiff boat.

Future upgrades:
Jib adjustment system: There are numerous upgrade kits. Requires adding cleats and turning blocks.
Comp Tip: Class required modification to your mast. You can get away without it for a while but it is required. You can butcher your existing mast or buy a new factory mast w/ CT and then sell your old one.
Aussie halyard system: Reduces mast compression and allows easier rotation in light wind.
Rudder upgrade: Replace the crappy Lexan rudders with the FRP "racer" rudders. Mucho $$.

New parts are available from many sources: Cat Sailor website, Hobie, Murrays and Sailing and Ski Connection in Myrtle Beach. Used parts can be had from Dan "Cat Reaper" Berger in Virginia Beach.

SC is in Division 9 of HCA of NA (is/was NAHCA). Loyd Graves in Raleigh is the Division Chairman (e-mail addy at the class website). Also consider attending the Spring Fever Regatta on Lake Hartwell, GA on March 25-27. SFR is the early spring Woodstock of cat racing. Show up even if you don't intend to race. You can get enough free advice to fill a book!

This forum is an excellent resource. H16 sailors of all abilities, including some very experienced racers, post here. If you have questions, please ask. Sailors here love to relate their experiences and dispense free advice . The forums at Hobie Cat are also a good resource although I would say they are more focused toward general interest than racing. Welcome aboard!