I don't think you can go wrong either way. The LL Bean Quest reel is graphite composite (as opposed to the cast metal Medalist) but it's supposed to be a decent reel, and it's actually the same reel as the GREY GLA 80, which normally goes for around 60 bucks. Bean also offers a 100% customer satisfaction guarantee on everything they sell, so you really can't go wrong.
For the Quest preloaded version, you’d want this one to match up with your rod (the reel is a quest size 2, with a 5 weight line, backing and leader installed) for 59 bucks:
Preloaded Quest II #2 Fly Reel with 5 Wt. Line: L.L. Bean Reels at L.L.Bean
I also have a bunch of Pflueger Medalists that I've been using for 30+ years, so if you want to go that route, it would also be a very good option. For a Medalist, I would order one from Ron at Hook & Hackle Fly Fishing Tackle, Fly Fishing Supplies, Fly Tying Supplies and Fly Rod Building Supplies
and get a Medalist Model 1494 about 25 bucks, and one of his "overrun" 5 weight, weight forward floating fly lines for 25 bucks (normally 55 bucks). You'd also need 20lb backing (hook and hackle 20lb dacron 7 bucks) and a leader (3.50). (If you were to call Ron on his 800 number he could pick it all out and rig it all up for you.)
The price would work out about the same either way, for the preloaded Bean Quest or the Pfleuger + flyline, leader and backing. Either one would make a fine outfit for you, and you'll have a blast.
It sounds like your tech teacher is into fly fishing. It's great to have someone that you can get a few pointers, and maybe some help with casting if you need it.
Good luck, the fishing will start to heat up pretty soon.