In the Sierra, wilderness permits are always obtained for your entrypoint, and with the exception of the Mt. Whitney area, your permit is good for the entire trip, no matter what areas you travel into. Only the quota for the entrypoint (if it exists) applies.
For the JMT, the two endpoints (Happy Isles, Whitney Portal) can be hard to get permits for, as they both have quotas and tend to fill early--especially Whitney Portal. A weekday start helps a lot. Availability is listed and updated on the Yosemite NP (http://www.nps.gov/archive/yose/rptFullTrailheadDates.htm) and Inyo NF (http://www.fs.fed.us/r5/inyo/recreation/wild/otheravail.shtml) websites. Both Yosemite and Inyo allow reserving permits in advance for a small fee. Unless you are a purist who wants to do the entire JMT, you might consider a less-used trailhead.
For a southbound trip, some alternatives are the Panorama Trail (Glacier Point), Mono Pass, or Silver Lake/Gem Lake. (Lyell Fork is as popular as Happy Isles, thus why it's not included here.) Before the JMT was constructed parallel to the Mist trail, it followed the Snow Creek trail out of Yosemite Valley, providing another, historic alternative, especially if you start at the sign in Curry Village noting the original location of the LeConte Memorial, which is the historic start of the JMT. Devils Postpile/Reds Meadow is another alternative, but you're bypassing a lot of scenic country starting this far south.
For northbound, there are fewer options: Cottonwood Lakes/Army Pass is probably the best way to bypass the Whitney Zone. A creative, long, and beautiful west-side start would be to use the High Sierra Trail in Sequoia NP to reach the JMT.
Oh, one more thing: proper food storage is required along most of the JMT due to black bears. In practical terms, this means you'll need an SIBBG-approved (http://www.sierrawildbear.gov/foodstorage/approvedcontainers.htm) food storage device, since fixed lockers and trees suitable for hanging can be hard to come by. The Ursack Hybrid is the current low-weight champ, but its approval status is uncertain (http://www.ursack.com/ursack-update.htm). Yosemite, Sequoia, and Inyo's websites all have their current food-storage requirements.