Differences between MM or MC/Recommendations?

There are quite a number of very good cartridges now in either MM or MC configuration. Or even moving iron. I am sure that you could find a good selection in either category. Many purists will say that a top MC type will give more detail and quicker response. I tend to agree with this and have a MC myself. However MC have drawbacks too, like needing more step-up which adds either a transformer or more gain stages to the signal path. High output MC are very popular lately, as a compromise between both types. It is more important to get a cartridge that you like the sound of, and mates well with your system, than whether it is MC,MM,or MI. Just like it is with any other component, the execution of design, and the system compatiblity, may be more important than specs or theory. IMHO.

There are good units in both types and Twl said things pretty good. If I could add through my experience over the years with both types, though no real generalization can be made due to the enormous offerings in both, I will say that I find most MM's I have used to be warmer in sound and the MC types to have more sparkle and clarity. I prefer most MC's I have used to the MM's but that is just me.

and with a rega table, i recommend dynavector cartridges. they seem to blend perfectly with the planar series for some reason. i used to run a 10x4 w/ a planar 3 and it sounded fantastic. i'd look at the 20x, which is available in high or low output versions.

In your situation it would be more reasonable to spend only half of your budget for the cartridge and the other half to place either inside the pocket or upgrade the phono stage.
EAR 834P, Trichord Delphini, Trichord Dino and also Benz PP1 is on my list. The cartridge I would recommend is Benz Glider or Dynavector 20Xl.