Answering my own question for posterity: (This is all for US shipping info)
1. Packaging: Bubble Mailers ended up working pretty well, and I ended up bubble wrapping my kits and then placing them in the bubble mailer for extra bubble protection. However, for added sturdiness I purchased small boxes on the cheap. I asked at the Post Office if these 5″x5″ boxes might be too small, but I was told that they should be fine and that I could go even smaller.
2. Cheap Rates: USPS First Class Parcel is the cheapest rate that I’ve found, although I wasn’t able to print and ship labels directly through USPS (I’m not sure why they removed that option). However, I was still able to print First Class USPS labels through Paypal here: http://www.paypal.com/shipnow
3. Other tips: Make a spreadsheet for order tracking! I made the mistake of offering Venmo as an alternative payment method for my kits (instead of purchasing through the website), and now I need to keep track of all my sales through various channels! In the future I’ll plan to sell my art explicitly through one avenue, but having a spreadsheet to keep track of which orders are in progress, which have shipped, and their tracking numbers has been a helpful tool.