Epoxy would be terrible. In speakers you have to slide boards down the dato channels. Braces, and the internals of TLs and horns need to slide in and Titebond actually makes them slide easier. Once epoxy coated surfaces touch, they ar generally stuck, especially once the hardener starts to work. Titebond does not really start to set until you put it under pressure. Then it sets good and hard fast. Don't even think about building a speaker from anything other than those water based types of glue
I could not think of a worse glue to use to build a speaker than epoxy and contact cements.
I prefer titebond original for all wood gluing for the same reasons you shared. The stuff is liquid gold for wood working. Just make sure you get some wet paper towels ready for cleanup. I've used this stuff for fixing a bed, a dollhouse, and making speakers. It's something a man should have in his house in my opinion. Make sure you clean up the applicator really good after use. If you get it on your hand you can just rinse it off in the sink. I still prefer using disposable gloves when handling it, but it's safe to get your hands dirty around. You can clean it off your clamps too.
Clean up is a huge deal for speaker gluing because you will want to use a lot of glue. In this contest Titebond Original is among the best.
Start simple and get experience!
Supplies to start with
Madisound Recession Buster Kit,
Circular Saw(get a forrest II blade)
Framing Square
Jasper Jig(this tool is amazing and is my favorite tool to use.)
Plunge router w/spiral upcut bit(get a whiteside bit)
Good work bench
A drill with a straight drilling jig of some type. I got one for around 20 bucks at home depot. It's not super awesome, but it does the job for drilling a straight hole.
As many clamps as you can find. Corner ones, Quick Clamps, Bar clamps, etc..
Go with 13-ply if you want something easy to move and light. Go with MDF if you want something cheaper.
You can buy sectioned down ply at home depot or lowe's. I get 2' x 4' sections of 13-ply.
There are other tools you'll want along the way but that's a good start.