Beginner Turntable

I can answer some of your questions.
As far as using a TT with the Denon RCD-M39s, I see there is one analogue input for an external device.

But the output level of a TT is very low and cannot plug directly into the Denon. You would need a phono preamp which boosts the volume of the TT and then plugs into the Denon amp. Now you would have a signal from the TT that is high enough for the amp to play it. Without this preamp, you would not hear the TT thru the Denon amp.

I would suggest looking at a TT that has a built-in preamp.
Then you would save some money and be able to plug right into your Denon.

Many online stores sell turntables that include preamp and cartridge.
Here is one example...

http://turntablelab.com/collections/turntables-with-built-in-preamp-alpha/products/audio-technica-at-lp60-automatic-turntable-pre-amp

That said, the difference in your mini system won't be audible or may be subtle at best. Don't overspend if you are going to keep your mini system.

Meaning that since you have a budget sound system, it would not make sense to buy an expensive high-end TT and cart. You would not be able to fully appreciate the high quality sound and the benefits that come with it...such as more detail, better dynamics, less surface noise on the LP.
If you were to upgrade from the Denon mini to a more revealing system, then you could easily hear the difference in sound quality between TTs and carts.

So if you are planning to upgrade from the mini in the future, then you should buy the best TT you can afford.