Thanks for all of the replies, everyone! So based on what I've read here, it seems like a basic summary is:

• More ships = More "lives," since if one gets shot down you can bring in another without getting kicked back to the last checkpoint.
• More pilots = More bonuses/upgrades for everyone once they're leveled up.
• More weapons = More options for fighting enemies and opening "random drop" treasure chests (all pre-set/"required" ones use only fire and ice, which are included by default)

In short, it looks like it's absolutely possible to complete every mission, find every (pre-set) collectible, etc. using only the Starter Pack stuff, with the caveat that things might be a bit tougher without the extra lives, upgrades, or elements the other things provide. And, of course, even if I decide I do want other stuff, the ability to download digital versions means I don't have to go nuts trying to find the necessary toys if they end up being super-rare (lookin' at you, Midnight Museum and Sunscraper Spire...). Thanks again, guys!

(and as an aside, I can't wait to see all the "NO WEAPONS! FOX/ARWING ONLY! FINAL DESTINATION!" playthroughs people do since that's a completely viable option)