Fresno Yosemite International Airport (FAT) would definitely be the fastest! Plus Fresno has a lot of great shopping and restaurants and you could check out the Forestiere Underground Gardens.

If you're just going to Yosemite, I would just fly straight to Fresno Yosemite International Airport (FAT) since that's about an hour drive away from the park.

I'd only fly into the other ones if there were things or people who you'd like to see there or if it was significantly cheaper because they're 3+ hour drives away. Sacramento International Airport (SMF), San Francisco International Airport and Norman Y. Mineta San José International Airport (SJC) are all equidistant from Yosemite.  Oakland International Airport (OAK) is another big'ish airport that you could look into and is a little closer.  Also keep in mind that you might encounter a bridge and bridge toll if you go from SF, depending on your route.

I don't think any of the 3 airports should be an issue. You will probably pay more  money flying out of SF as it is father away and you will have to drive through traffic both there and back. 

Personally, I'd just price out tickets and rentals and go with whatever was cheapest.