Your statement of “I have a few of each type” would lead me to look at the MM/MC phono preamp option. The premise for that choice would be the multiple MC cartridges and their individual requirements for optimal performance would not necessarily be provided by a single SUT. Many phono preamps with MC ability provide multiple loading options and possibly multiple amplification settings that would be more versatile in you described situation.
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Most of the phono stages on the market are MM/MC.
If your cartridge is 0.2 mV or higher you can use it with most of the MC phono stages, for lover output you will need a phono stage with higher gain.
SUT is a different flavor, only you can decide what you like with your carts in your system.
Matching SUT to a cartridge impedance is also very important, this SUT for example can handle carts with 3 - 40 Ohm impedance range.
In my opinion you have to start with MM/MC phono stage, you need an MM phono stage for a SUT anyway.
P.S. Besides the SUTs you can use active headamp (with all LOMC) or very special current-injection phono stages (for low impedance MC only).