Hello and welcome to RTA !

Three weeks is a nice amount of time for the trip with time to get an overview oof the places you are visiting. As you may know the Tioga pass [CA120] could still be closed in the Spring, but the way you have mapped your route from Death valley to Sequoia to Yosemite would suggest you have decided to go around the south of the mountains anyway.

As you are doing a loop it doesn't really matter where you start but the direction you have is good in the fact that heading south from SF will put the Ocean on your side of the road. You could base your starting point on whether one or the other [Vegas or SF ] is cheaper to fly into and rent a car from.

I'm not sure what your plans are between MV and Bryce, but you could head up the Moki Dugway[UT261] and through Hanksville to Torrey and then on Utah scenic Byway 12 through Escalante. That will take you past Natural Bridges and Capitol Reef NP as well as the wonderful drive along scenic 12 and the 'thrill' of the Moki ! [Use the search function] ;-)