Some time ago I bought a mandolin too, an Appalachian, or more properly termed (I suppose) Bluegrass model, which I prefer due to the fancier accoutrements (and F holes!)
I do love the standard tuning of Mandolin- fifths, which resembles a violin, viola or tenor banjo, and play the instrument in groups as a lead or accompaniment instrument. I also like to experiment with some other common tunings or even my own alternates for various improvisations.
I'm certainly no expert, but I can confidently say that Tremolo is all from the wrist- for sure! For me the most important thing is to keep the wrist relaxed and keep breathing, rythmically at best.
Have fun- it's a marvelous instrument which is uniquely beautiful and virtuosic at times. It never ceases to amaze me how small the neck is, yet this doesn't limit its playability at all once it's learned (or hacked up) a bit.
I handed my mandolin to a slightly more seasoned singer/songwriter compatriot of mine at a recent jam session, who'd never played one, and he was almost instantly ripping chords and leads that sounded like he'd played for years!
Have you heard the Zeppelin tune "Battle of Evermore?" As I understand, Page made this up on the spot having never played the mandolin before. Of course that would have been a Folk or Celtic mandolin, and I believe Jones wrote some material on this fantastic instrument as well.
All that being said:
"Pay no attention to what the critics say. A statue has never been erected in honor of a critic." -Jean Sibelius