do I have to stick with MM or can I move to MC...?Technically, there's no reason you couldn't go to an MC.
... and would I want to?Possibly, but as Tobias and others have tried to advise, it would be an error to move very far up the cartridge hierarchy for the TT and tonearm you're considering. Keep your cartridge budget under $500, maybe under $300 and you'll be fine.
High outout vs Low output, Are there advantages to one over the other. I understand how they work, but sonically speaking what can I expect?As a rule, LO MC's have shorter/thinner coils on the cantilever vs. their HO cousins. Lower moving mass results in increased speed, responsiveness, HF extension and micro-dynamics. These are all good things and will let you hear more of the music in the grooves, PROVIDED the rest of the system is up to it.
The rig you're considering is not up to the performance levels of most LOMC's, certainly not the expensive ones costing $1K+. What you'd hear if you bought one of those would be the limitations of the table and arm, not more music.
LOMC's also require more amplification from the phono stage to boost the signal voltage up to levels your line stage can deal with. The more amplification you need the higher quality the amplification must be, otherwise you'll hear problems or limitations in the amplification chain instead of better music.
Finally, LOMC's require fairly careful impedance matching. All MM cartridges and most HOMC's are designed for playing into an MM's phono stages 47K ohm load. That is not true of LOMC's, and there is no standard from one to the next.
FWIW, my advice is to stick with MM for this rig. It won't pay you to move much higher. If you must try a LOMC I'd suggest one of the venerable Denon 103 series cartridges. They're about as non-fussy as a LOMC gets.