Recommend an Entry Level Turntable (And maybe an integrated Amp)

Just another response of someone suggesting random components to look at, but for an affordable phono stage check out the Project Tube Box S2 and replace the tubes with Gold Lions. Definitely a big step up compared to a basic phono in an integrated amp and really fleshes out a great sound when paired with most any cartridge. It's certainly not the best in the world but it'll allow you to not need an upgrade for quite a while and still allows a big budget for the rest of the system.

I get you're still happy with the Denon, but I'd also suggest you upgrade that receiver first. You will hear a big difference with the NAD (NAD always sounded better then Denon in my opinion), or any of the others mentioned -  for CD's and streaming even, much less a new turntable. The phono pre-amp in the Denon is a weak link, not just the power, or age of the whole thing. The Project is a decent table for the money, but I doubt you'd be happy spending more money on a table right now as it probably won't make much difference with that receiver - good in its day, but that was a long time ago. 

As for turntables, I own a REGA, but the other ones mentioned are fine also. Just one opinion, but I hope it helps.

Agreed, upgrade the integrated. Look at the Audiolab 6000A. Fully featured, wonderful sound, reasonable and a nice built in phono section. My fave except for maybe the Parasound Int. I would say don't cheat on the cartridge either. I see a lot of nice ($500.00+) turntables sporting a $79.00 cartridge. My old rule of thumb, crude as it may be, is 25-30% of the TT cost for the cartridge. That's 70's thinking but that's when I started in to audio...

If I were in your situation, I would look at the Denon PMA-110A.

It’s the real deal.

This is the anniversary edition of this 2ch integrated amp.

It has an excellent partitioned dedicated phono section.

80 watts into 8ohms and it doubles down to 160 watts into 4ohms

Stable to 2 ohms and will push a 1 ohm load.

Dual mono: two transformers! 

Its not cheap (just under 4k) but it’s a poor man’s Luxman.

Then get a $1000 turntable. If you can push a little higher, the Technics 1200GR is tough to beat.

I do not want to rain on your parade but it is very unlikely that you will find vinyl gear which is likely to sound anywhere as good as digital, unless you spend some serious cash. Simply by the limits of the underlying technology involved, vinyl will never be able to match the dynamic range of a CD. And a new amp will not make that much of a difference. The limitation is at the source.

If you still must, check out direct drive Technics turntables for probably the best price for value and reliability.