In crazy low-budget "10 songs in 10 hours" sessions like the one your describing, it's my opinion that you have to make do with what you have. Having extra snares lying around included, though. It's always good to have backups for the neighborhood garage bands but that's not really your job, nor is it your job to waste 3 HOURS trying to get a snare sound! I'll assume that you're exagerating.
Anyway, I like to think that all instruments have a place. Pawnshop gtrs hold a dear place in my heart. Kays, Harmonies, Airlines, Hagstrom. They all sound special and different, just like nice Teles and Les Pauls. Same is true for drums, of course. Nasty trashy snares can be fun to mess with and cool in the mix. It's the engineers job, especially in these budget types of situations, to make due and make the best of it, good gear or not.
That young inexperienced drummer is responsible for "his sound." Every bit as much as Bonham was for his. He made conscious decisions for years leading up to the session developing his kit and playing style. Perhaps he's not the dummy you might think he is simply because he doesn't have a snare like the one you heard on a record you liked! On the flip-side of that is bands can't walk into the studio and expect to sound exactly like records of other bands they've heard and liked. It's just not possible.
I try to trust the people I record. That doesn't always work, but part of being a good engineer is to know when to step in, how to affect the situation in a manner that makes everyone happy (for instance you don't want to make a guy used to playing a crappy tele knock-off and pretty much lovin' it play the studio's brand-new Les Paul), and how to not spend 3 HOURS doing it! What a buzzkill for the band, especially the poor drummer, that must have been!
Understanding the fundamentals of drum tuning is a must. I can't play a damn thing on the drums but I can re-skin and tune a kit in no-time. Just practice it. You'll never need half the stuff you'll learn from doing it but you'll understand the basic rules of the thing and that's usually all you'll need to make quick, subtle adjustments during set-up to improve the sound.
As for back-up snares, check out a bunch of second-hand snares. Buy the ones you like. Any drum can be made to sound good. If you must have something new, DW has a budget line called Pacific, they're mighty nice for the price.
Versatility? Different drummers will all sound different on the same drum. That's pretty versatile!