Of all the places to resupply, Edison Lake (VVR aka Vermillion Valley Resort) makes the least sense. It's a long 5-6 mile hike off the JMT, or a $20 ferry ride (in August the lake/reservoir will be quite low, so longer hike to the ferry, too.) Lots of people like the camaraderie and atmosphere at VVR, but you will be in a group, so you won't really be lonesome. I think I've heard many hikers will spend $100 there with the great meals and good beer -- just depends if that is what you want.
It makes better sense to resupply at Reds Meadow. There is even a shuttle bus right from RM out to Mammoth (30-40 min. ride?) so you could go out and buy supplies there. (Incidentally, it's a good place to park your car, too, since YARTS shuttles Mammoth to Yosemite, and ESTA shuttles from Lone Pine to Mammoth.) I'm not sure what the store at RM has, but you might just buy supplies there.
Tuolumne Meadows: there is a store there as well. Not sure what hikers have to say about selection and variety, but buying supplies there is an option, too.
So you see, Krishna's resupply spots make sense. It would be up to you to decide whether to run out over Kearsarge Pass to try to pick up more supplies in Independence -- that would burn a full day, maybe even an overnight. You might consider that as an option, and decide once you get there, based on the progress and speed of everyone in your group.
As for mailing yourself supplies, the U.S. Postal Service has flat rate boxes you can mail from anywhere in the U.S. to anywhere in the U.S. 12x12x6 (Large Box) is $16.
