Turntable - The Next Step

@gnoworyta  I only ask because a great tonearm will extract more from your cartridge. You could upgrade parts of the P3 & rewire/mod the tonearm...or get an Audiomods Classic III tonearm. 

It is time to Travel and receive demonstrations, if this is an option that can be considered.

Using ones ears is the most valuable method to make prepare for making an upgrade.

The familiarity with the owned TT Set Up will allow a immediacy to identify with an attraction or detractor during an demonstration of an alternative TT Set Up.

If you can make an arrangement with a premises that offers demonstrations to allow you to bring your set up to be used for comparison, this is a very good start, a home demonstration is even better but not as easy to get offered.

Make a Box to transport your TT safely, bring your Phonostage to a premises that has offered a TT demonstration, and have this used during the demonstrations, an alternate Phon' can also be introduced as well to extend the experience.

Transit and time does have a cost, but it is nominal and the absolute fundamental requirement to assess what is attractive to you without laying out large sums to find out the purchase is not too impressive.  

Not rushing into this will be good, and if a few items of interest can be discovered through the forum all is well and good.

If you're asking what single upgrade would yield the most cost-effective benefit to SQ, I'd suggest a new cartridge.  Another bang-for-bucks upgrade would be to get an LPS to replace the wall wart on your phono preamp.  MS sells one that would be compatible with any other pre in their line-up.  You could also go (much) cheaper with a similar voltage after-market LPS, but as with all things audio, you may not get as much improvement.

I'll second the Music Hall MMF-7.3. It's a fantastic turntable for the money. To me, the Ortofon 2m Bronze it comes with is one of the best cartridges I've heard at that price point. It does everything right in my book. I have the MMF-7.3 In walnut veneer, which I like better than the black. It is a very well thought out design. I pair it with a tubed phono preamp, the Tavish the Classic with NOS tubes (RCA 7025, GE 12au7, and Sylvania 5751). 

I was quite shocked when I threw caution to the wind and upgraded my turntable set up from the Rega P3 to a Clearaudio set up. The sound stage and overall improvement in the clarity of high and low frequencies was outstanding. Good luck.