Non Rega cartridge suggestions on a P6

Rega cartridges are ONLY 14mm height. Most cartridges are taller than that, say +/- 17mm.

To keep the tonearm parallel to the LP when in play position, which is the basic rule to get VTA correct, we usually raise or lower the tonearm. Rega tonearms are NOT height adjustable, they and others sell SHIMS to put under the arm to raise it up, i.e. 3mm higher for this one:

Shims let you choose nearly any cartridge height, thus your choices are vast.

What is your budget? Type: MM or MC or MI? Are you equipped to play low output moving coil (LOMC)?

A circular shim requires the complete removal of the arm, to pass the wires thru the circle, then re-mount the arm.

These ’split’ shims allow you to simply loosen the arm's base plate, slide them in from both sides, and re-fasten the arm.

https://www.acoustic-signature.com/products/accessories/rega-spacer-set/

Ortofon now makes 14mm high cartridges specifically for Rega Tonearms, the 2MR Series (7 options) (no shims required).

https://ortofon.us/search?type=product%2Cpage%2Carticle&options%5Bprefix%5D=last&q=2mr

There are some who think adjusting the height is not really important, I disagree obviously.

My experience is limited, but from memory I believe you would be safe with many Audio Technica cartridges and Ortofon makes a line of low profile cartridges specifically designed for Rega arms.  What you should look for is a low profile in particular.  

Nagaoka, Benz and Dynavector cartridges tend to sound good on the P6. If you experience dust cover issues, the best solution is the Rega 100 gram tungsten weight, which also improves the sound quality of the table. I believe the standard counterweight accomodates cartridges up to 14 grams which should be sufficient for most cartridges that are a good match to the effective mass of the Rega tonearm.

The tungsten weight is mainly needed due to its smaller outer radius…a shim greater than 2mm will cause standard counterweight to hit the dustcover. 
Rega could solve all these issues if they cared to by making their dustcover taller and making their arms height adjustable, but they evidently don’t care.