Which SUT? .... for .3mv/10 ohms MC cartridge into 3mv MM input sensitivity

20x would be a good choice for your 0.3mV 10 ohms cartridge, as well outlined previously. If you want a versatile SUT for other MC cartridges, then the Bob’s Devices Sky SUTs come with 2 gain settings. So either a Sky 30x/15x or a 40x/20x would be extremely versatile. I have a Sky 20/10 and Sky 40 myself; they’re exceedingly nice sounding boxes that work equally great with different cartridge makes.

You do have to watch out for MC cartridges that have a high coil impedance relative to a low output level. These can be trickier to match with a SUT since the higher ratios you’d normally use to bring up the low signal level will end up loading the coils down too heavily, which results in a significant loss of signal (i.e. you’re spinning your wheels or worse by going to higher SUT ratios). One example of this would be a Benz Ruby, with 38 ohm coils to 0.35 mV output (3 - 10 ohms is more typical at this output level). If you hook that Benz into a 40x you’ll lose over 7 dB of signal from loading down the coils (20dB * log(29 ohms / (29 + 38 ohms)), where 29 ohms comes from 47,000 / 40 / 40) - in effect, the net output is more like what you’d expect from a 15x SUT, and likely with other significant sonic aberrations to boot. However 40x on a 0.3 mV, 5 ohm Koetsu (which I’ve used) works just great. You could however counteract this issue with an MM stage that allows input loading settings above 47,000 ohms - which unfortunately is probably less common than it should be.

On the other side of the spectrum is the Air Tight / My Sonic Lab cartridges, which have a very low coil impedance relative to their output levels. 

I wouldn’t worry about 6 mV signal after the SUT being "too high" - most decent MM stages will handle that perfectly fine, and personally I don’t like being in the reverse situation where I’m pushing my preamp volume control too high and still wanting more volume. And keep in mind you will often lose around 0.5 - 1 dB or so from the cartridge being loaded by the SUT - depending on its coil impedance and SUT ratio - so in the case of 20x and 10 ohms coils you lose 0.7 dB of signal from the loading, so that’s actually netting you about a 5.5 mV signal (down from 6 mV) anyways. 5.5 mV is pretty close to ideal for most MM stages.

Heck, my 0.3 Koetsu into a Sky 40 sound awesome on my VAC MM stage, and that’s netting over 10 mV of signal after the SUT! You certainly don’t want to overload the MM stage input, but good stages have lots of margin and will still sound good until you’re way off base.

I also wouldn’t worry too much about hitting a specific target loading number with a SUT. You definitely want to avoid loading the cartridge down too much, keep the load at least 6x - 10x the coil impedance. But beyond that, it’s mostly about choosing a ratio to the right output level. It’s not like active MC stages where you can get obsessed with finding the "perfect" load number. Once you get a good SUT match you will hear it and be happy! Recommendations from those who have your particular cartridge can be very valuable. But like I said before, the Bob’s Devices Sky have been great all-’rounders from what I’ve thrown at them.