The Technics SL 1500C mentioned upthread is really rather crappy compared to your initial three considerations. If you could stretch your budget, I would look at the SL 1300G which dispenses with all the superfluous nonsense you usually see on Technics turntables and you could use any cartridge you want.
I would snatch up the P3 RS as a second turntable in an instant having owned an RP3 with a TTPSU for years and wore out several Exact cartridges on it over that time. Rega cartridges are very nice and you might consider the one equipped with the RS end game after living with it for a while but if not Ortofon has a 2MR range here https://www.musicdirect.com/shop/?query=ortofon%202mr just for the Regas because their turntables and arms are so popular. Everything Rega markets also has a lifetime warrantee even if you buy it used, though anything with modifications would be excluded.
As for the Mitchell, if the spirit moves you go for it bro! Find a reputable vendor in the US that distributes it and go with their recommendations regarding the appropriate cartridges to use with it which I’m sure includes Regas and the Ortofons I mentioned above. Covers are optional but you could find a decorative cloth or something to throw over it when not in use to protect it from dust and you might even like the esthetic.

