Hi Danny.
With 14 days in total you can make a great trip, but I would encourage you to look around a bit and make the trip your own, that's the magic and freedom that the road trip offers.
Here are some of my thoughts though. I would check flight and car rental costs into any of the 3 City's as it doesn't really matter where you start in the loop, but there are a couple of good reasons to start in Vegas. When travelling this time of year one of the most spectacular mountain passes that crosses the Sierra Nevada closes around this time of year due to snow fall and by heading from Vegas to SF via Death valley and Yosemite early in your trip you will hopefully get across the pass. If not you can head around the South of the mountains but Tioga is spectacular. The second reason, and the one that might answer the question that you could already be considering [what's the difference SF >LV or LV >SF] is that when heading between SF and LA the Ocean and Ocean side pull outs will be on your side of the road heading South.
When planning you need to consider that 1 night in Grand canyon [for example] means that you will only be spending a few hours there as it is a 5 hour drive from/to Vegas and a full day on the road from LA.
To start your planning off, this may [or may not] help and remember you can start from any City. LV 2nights > across Death valley and stop 1 night to the East of the Sierra's.[Lone Pine, Bishop, Mammoth etc] > continue to Yosemite 1 night > explore more of the park and head to SF > 2 Nights > Down coast to LA 2 nights > LA 2 nights >to GC 1 night > Visit GC and stay nearby 1 night >Vegas for another night.
Play around and when you have things outlined we can perhaps help to 'fine tune' your trip.