Turntable help, please!

I'm at a turntable fork-in-the-road - any advice appreciated. 

I'm looking to add vinyl (mostly my older albums, average condition, that have been stored for 20 years or so) to my system (Primaluna EVO integrated, Schitt DAC, Fritz speakers, Cambridge CD transport).  I've got a Denon DP-30L from the 80s that works fine with an old, probably inexpensive Grado cartridge (no model identifiers, silver body, black front).  Should I clean it up and use it (thinking cable replacement, motor service) or head into the brave new world of contemporary tables?  If keeping, should I replace the cartridge, and what would be appropriate to match the table?  I'd like to stay MM or high-output MC

In current gear, I'd appreciate recommendations for a new turntable.  A quick look indicates a lot of nice equipment in the $1500 range that would seem to suit the overall level of my system, though I could be persuaded to up the budget for clear improvement.  Used is fine.
Thanks for any advice!
I would definitely clean up the Denon and see how it sounds. If you are unsure of the stylus and think it needs replacement, get a replacement stylus. You won't have any/much money into the resurrection, so you can always still buy something new if you are unhappy with the Denon. Also, the Denon will then be in re-sell condition, so you'll have that going for you.....
Your Denon is good enough a lot of the magic will come from the phono stage. Since you want MM or high output MC then the Decware ZP3 will absolutely kill it. Instantly loft your analog front end to top of your system performance. Then clean and lube, DIY, https://liquidaudio.com.au/denon-dp-30l-turntable/ Not hard at all. Mount a decent cart, maybe some day down the road re-wire the arm, or put the table on Townshend Pods, tweak it out with some fO.q tape, you will be blown away how good your records will sound!
Clearaudio Concept is what I’d do at that price. A lot of table technology there. Probably more than you’ll get from any other manufacturer sub $2k. 
I had the Marantz TT 15-S1 (built by Clearaudio) also in that price range and enjoyed it. Recommend. 
+1 on the Clearaudio Concept and Marantz TT 15S1. I have both and they are sold performers. 
I encourage you to try the refurbished route first.  

If you don't enjoy listening to vinyl - I'm sure someone would be happy to purchase your refurbished table for more than it cost to refurbish.

About 5-10 years ago I dusted off my Dual turntable and had it 'tuned up' and used it enough to have me explore other upgrading the cartridge.  Ultimately I went with buying a Rega table and traded in the Dual for more than the refurbishment and what I bought the table for new in the '80s.
+1 on this. I would get a new stylus. An old worn stylus may damage your records. After that you can decide if you want something new

I would definitely clean up the Denon and see how it sounds. If you are unsure of the stylus and think it needs replacement, get a replacement stylus."
That's a nice old TT,  I like the stop and auto lift feature.

I vote for

1. a new MM cartridge, advanced stylus (microline, shibata, sas) and

2. cartridge alignment tools and skills (watch a friend, learn to do it yourself) (needed for any cartridge, more important for advanced stylus shapes) Good enough inexpensive tools and on-line videos show how to do it.

3. proper cleaning of your old records. I finally learned how, makes a huge difference. I clean mine manually, batches of 10, see photo of my setup in my LP listing


4. keep Denon DP-30L

a. change the cartridge

b. listen.

c. IF IT AIN"T BROKE don't fix it.

d. If handy, I would try some of the DIY things, probably not all.

I recently embarked on the same search in the same price range.  Because I had only used Bang and Olufsen turntables that you don’t adjust much, I also spent a lot of time learning about turntable and cartridge set up.  I settled on Mofi Studiodeck.  It has good reviews.  If you get it with one of their cartridges, it comes set up already.  But, it is fully adjustable if you want to change cartridges later.