I dug out my first race bike this morning. It’s time for some rehab work to make it functional again.
I’m sure what to do yet. I’m thinking a tear down and then spray with matte black plasti dip. Drop bars and 10 speed shifters with an updated wheel set.
I’d keep the frame as is. Keep it retro. Put on a modern(ish) gruppo, wheels, and cockpit. Oh and saddle.
Pads above the saddle. Le sigh. And road brakes turned upside down. 
Things sure have changed since then.
Definitely don’t change the paint job, unless you send it off to have the paint restored to look new, but the same, and have the fork match the frame paint. I’d then put a modern front end on the bike, maybe even grabbing a retro Look stem (with the two linkages) to get the front end lower. Tririg brakes front and back, Solid aero chainring. 1x?
And last, say you get the frame’s paint restored, get some new HED tri spokes at 25mm wide width at the rim and have “Specialized” painted on the spokes like below:
Defo don’t repaint unless it’s completely trashed.
If it’s trashed, repaint and regraphic in the origional theme
WD
Clean and repack front/rear hubs.
Continental GP4000 tyres.
Looking at your ‘fit’, I would suggest a flat-bat conversion and using it as an agile little town bike. Is it 2x7 speed? Maybe swap in a pair of Tourney flatbar shifters/brakes, they’re cheap.
There’s no point in setting it up as a retro TT bike if that’s your fit.
Leave paint or restore to original. Back to drop bars.
I like the idea of trispokes.
Get some nice bike polish and make it shine.
I’d recommend going through here and looking at a few of the older bikes for ideas on restoration. You don’t have to keep it classic, but keep it coherent. https://cyclingtips.com/tag/bikes-of-the-bunch/
That pic makes it hard to tell how the fit is. The saddle is about 6cm below my fit and it has the old spring loaded flip up pads. When they are up in that position it looks strange.
I stripped everything off except for the square taper BB and forks. The BB is still smooth as butter but the headset feels like it’s grinding. The top tube has a small dent and the whole frame has some rust patches all over. Nothing structural but it it for sure needs to have something done to fix it.
The crank set is Shimano 600 FC-6400 and they look pretty good so I think I’ll reuse them. I have a set of Dura Ace 7800 10 speed shifters that I think I will use also.
About the only thing I need to buy is a 10 speed rear derailleur and new chain.
I just need to figure out what to do with the frame at this point. And how to fix the headset.
Good work. A quality square-taper BB will last for decades, no point swapping that out.
It’s also easy to fashion a headset press with a length of threaded rod, some nuts and washers, and whack in a new cheap threaded headset. I’ve done that a number of times with good results and my wrenching skills are pretty crap.
I honestly wouldn’t bother with anything too drastic for the paintwork. Sand down the rust spots as best you can, then fill in with some nail polish in a matching colour.
Your existing rear derailleur (unless it’s a Dura Ace 74xx Series) will work fine with 10-speed shifters, the cable pull will be the same.
Best of luck!