What would you do?

Hey @thecarpathian I bought a Denon DP59L turntable recapped and restored from captmark09 on YouTube about 6 years ago and it's the best turntable I've ever owned (previously Realistic turntable, then Sony linear tracking, then Ariston QDeck, then Thorens then Project then Music Hall then Fluance, etc over the years).   It ended up costing me a little less then $1000 including a new AT VMN40ML cartridge he installed.  Mark was getting turntables from a Japanese contact and recapping and restoring them in Dallas.  I would say that, in your case since your turntable is functioning fine, I would just use it and enjoy it...then get it restored if you have a problem, maybe buy a new cartridge that you prefer.  It may not be your "forever" turntable, so I might not spend the money right from the start.  Enjoy!

If, like me, you have a hard time leaving well enough alone, be sure to get a good soldering station. I got a Hako a couple of years ago and love it.

Hello. I have a Denon DP-51F purchased new in 1980. Only repair needed was to r&r the interconnect cables.  I’m familiar with the 62L model.  If the speed is still spot on I’d suggest using as is.  I would also suggest doing a visual inspection of the caps prior to a recap. If any are showing signs of degradation a recap may be prudent. A properly running 62L is equivalent to $3-5K TTs in today’s market IMO.  I recall that unit has 39 caps in the speed control circuit which means almost 80 solder points.  If you have the skill/tools or know someone that you trust to do the work then go ahead (if you must). 
Enjoy the music. 

The capacitors are not in the signal path, so unless there's a speed issue, or tonearm problem I wouldn't worry. As to cartridges, mine runs a Shure V 15 type IV. The tone arm is less than stellar, in my opinion, because of the joints which may age poorly, and the electronic counterweight. Mine tends to rotate in and out of service as my whims, and acquisitions change, but for the age and the occasional bargain price, I would pass it by, unless there is an interest in vintage... Having said that, mine has been in service for thirty years, or so. The turntable was not designed with a long life in mind, more a happy accident of good engineering and quality components. At this point in its arc, it probably should, or could be considered "disposable", or as a parts donor if there is a breakdown.

I have a great turntable guru who has guided me through several of the turntables I've owned, the most recent being the holy grail Garrard 401 and then a pimped out Lenco 75. I'm moving next to a direct drive turntable (the Technics Sp-10 MK2 mostly for a simpler setup) but one of the tables that's pretty much in that league is your Denon DP-51. I think your tonearm idea is wise, and my only suggestion would be to consider the Denon DL-103R moving coil cartridge, which is not just a classic but one of the best values around. I used to own the Clearaudio Maestro and one of the Grado Reference cartridges (these are both in the $1,300 - $1,500 range.). In my experience, the MC world is another league and my DL-103R at $500 compares favorably with my $5,600 Dynavector XV-1s. Food for thought.