Some cartridge recommendations

Backwash, There are many MI cartridges that will work well with 50db gain or even a bit less.  IMO, after many decades in this hobby and after many many cartridges have passed through my hands, you are much better off with an affordable MM or MI cartridge than with an HOMC (High Output Moving Coil). Be cognizant, though, that some MIs are low output and some are high output.  Soundsmith and Grado make both types; you want an output of 2mV or higher.

Backwash, just to revisit the question of phono gain, you say your Modwright has MM and MC inputs. Then you go on to say gain is fixed at 50 db. That is not enough gain far an average LOMC cartridge, and it is way short of adequate for the MC10, which is among the lowest of LOMCs. If you move forward with this cartridge you are correct in thinking you need a SUT or some other way of supplementing total gain (e.g., a head amp or a current driven gain stage). If a SUT, you need at least a 1:20 turns ratio. Make sure you have enough gain before proceeding to conclude that vinyl is not worth the effort.

If the SP10 was purchased new by your grandfather and if it’s never been serviced and/or was in storage for many years, you might want to consider having it evaluated for speed constancy and etc. Check speed with any inexpensive strobe device. If it appears to work fine, you might get away with doing nothing. Electrolytic capacitors die with age and especially when left uncharged for long periods of time. Replacement is cheap because lytics are cheap. I’d go with a low or mid price MM or MI cartridge. Contrary to what was written above, you don’t need to buy an expensive LOMC in order to enjoy flat response out to and beyond 20kHz.

To unleash the expected flood of bewildering recommendations, what is your budget?  Also, try to find out what is the effective mass of your tonearm plus headshell.  (If you're using the OEM SME headshell, then usually the mass of the headshell is included in the manufacturer's spec for "effective mass".)  Then add the weight of whatever cartridge (typically 5-6 gm to less than 15 gm).  And you can then select a cartridge with suitable compliance to keep the resonant frequency within the accepted range of 8-12Hz.  (There are automated calculators on line.) OR, ignore all that crap and get a cartridge you like and can afford. In actual practice, most cartridges work with most tonearms, unless one or the other is wildly different from the norm.