Different adhesives for different jobs. It also depends a little bit on what you refer to as fast.
I would no more use CA (superglue) for all of my modeling jobs than I would a hammer for all of my woodworking tasks.
CA is a great adhesive, and very strong for most applications, but it’s not cheap. You can probably find cheaper prices on-line for 1/2 oz or 1 oz bottles than you will at a hardware store.
Tacky glue is another great choice. It’s basically white glue which has had a lot of the water removed. It holds pretty much right away, but takes about 6 hours to fully cure. Aleene’s (sp?) is a popular and widely available brand.
Walther’s Goo is a great, rubber based adhesive, which is strong but more flexible than CA, so it’s less likely to break off if accidentally bumped. You put a little on each side (or a gob on one side, then touch the parts together), then wait about a minute and join the parts. It grabs immediately, but full cure takes about 48 hours.
Epoxies are another great choice, especially where gap filling is required. They join parts after a couple of minutes, but again, full cure takes about a day.
For styrene plastics, basic modelling cement is hard to beat (I like the ModelMaster stuff that comes in a black square container with a long, thin applicator). Again, quick bond in about a minute, but full cure takes about 24 hours.
Often overlooked is the humble hot glue method. Not the strongest of adhesives, but it sets up very fast (seconds), and reaches full cure after only a few minutes. It’s cheap too. The biggest drawback is that you’re often left with strings of adhesive to remove.
All that said, my adhesive of choice for wood is basic old white glue. I have invested in a couple of different clamps (although a mini square and a rubber band works well too) which make it easier, but I’ve never had a problem.