I use CA for the quick place and hold work though it will fracture on impact most of the times.
Epoxy is ok but messy and can really degrade over time with UV exposure.
For really strong bonds, (Long term), I use a gorilla glue equivalent. Whilst it takes a lot longer to set/dry is has a penetration into the wood which is hard to beat. There is a trick though and that is to use less than you think necessary because if you use too much it will foam as it sets/dries and leave unsightly glue lumps everywhere.
I have not tried the Titebond III. It is more water proof, but I heard it is a little harder to work with. The Titebond II is a good compromise between the I and III, plus most builders prefer Titebond II from all the research on forums I have done. I really liked working with it and with the magnetic build system it gives you plenty of time to position parts before it sets up.