Ive used both Gorilla Glue, Liquid Nails, and a bunch of different types of wood glue, such as Elmers and Tite Bond. The wood glues are definitely the way to go for wood.
If its something really small, like a single 10 sealed on low power, you can get away with Liquid Nails as long as you screw it together nice and tight, but its still better to use wood glue in any application.
Tite Bond II (maybe III, I dont remember, maybe someone else does) was the best glue IMO. All the wood glues stick the same from what Ive seen, but it was either the II or III that was thicker, so it wasnt as runny which was nice.
Either use a nail/staple gun and clamps or screw it together. When screwing it together, its still easier to use corner clamps just to make sure the corners come together and dont push apart when you screw it together. I bought a pair and just use them to hold it together when Im putting the screws in, then take them off and move to the next one since the screws hold it together to dry.
When youre all done, unless your cuts are absolutely perfect and assembly is absolutely flawless, its always good to take a little bead of some silicone or Liquid Nails and smear it in all the joints to make sure its sealed.