I'm getting ready to send my resupply package to Muir Trail Ranch and wondering if there are common things that don't do well sitting in the resupply package for a few weeks. I'm specifically wondering about snickers bars and whether or not they will just end up as a melted mess by the time I pick up the package.

If you are sending to Muir Trail Ranch that means it's in a 5 gallon bucket right? They have or had a problem with mice and prefer hikers to send resupplies in 5 gallon paint buckets. At least thats how it was in 2009.
Anyhow i sent a lot of resupplies on my 2009 thru hike of the PCT. Never once did anything melt. I think you will be fine.
As for things NOT to send. I would never send myself oatmeal again.
I guarantee you will find pounds of oatmeal in every hiker box along the PCT and therefore JMT.
Also if you send yourself any powdered stuff life milk powder, gatorade powder etc. make sure to double bag them. The altitude change sometimes pops ziplocks and the powders leak out. of course they wont escape your bucket but for those resupplies you send in a cardboard box the result is mystery powder escaping. The Postmasters along the PCT know it all too well!
Have fun on the JMT! You are so freaking LUCKY!
I am really jealous!