Welcome to the forums! I'll start with the second question first, and yes I've trued my own wheels - many times
. Once you get the hang of it, and figure out the "tricks" it's actually a very pleasing - even fun - process. Some hints that I've learned, the biggest being to remember to never LOOSEN a spoke. That was my big newbie mistake last year
Also make sure you aren't turning the spoke itself, just the nipple. My final - and probably biggest - is to use a tensionometer. Spoke tension is half the game, from what I've learned, and many times this can save a lot of headaches.
Now, regarding your Giant, I have a slight bit of bad news. The reason you popped a spoke is quite simple - those wheels have too few spokes! Us big guys on 24 spoke wheels just aren't a combo that should be considered. I'd recommend finding a shop (maybe not your LBS, as you said they didn't have it setup right) that can build you a good rear, and maybe even a front wheel. The Velocity Deep-V is quite popular, but seeing that you are riding rail trails - which I'm assuming are gravel - I would recommend the Salsa Delgado rim coupled with a 36h hub (Deore/LX/XT all are great) and 36 high quality spokes.
Good luck, and enjoy the bike!