Based on my limited experience:
Glue dots (3/16") for adhering detailed chipboard embellishements and lettering.
ATG -- Just bought it the other day -- for all-purpose. The only reason I bought it is for the overall savings on adhesive. I liked the Tombow better, just because it's easier to hold in my hand and pack/store, but I was going through a crazy amount of adhesive.
Pop dots -- I'm not loyal to any brand, but I picked up a bunch of Recollections two weeks ago and I'll probably stick with those because they are the cheapest. I like to cut out the "negative" pieces for larger areas once I go through the dots.
Liquid Glue -- I'm going to try glossy accents because my hot glue gun hates me, and Tacky Glue isn't holding together my rosettes.
Scotch double-sided foam tape -- I use this in place of pop dots when I want *some* dimension, but don't want things in "3d".