Titebond and Titebond II along with CornerWeld, another adhesive of choice is the Maxim line, the 5/15 Maxim.
Sets up in 5 minute, bonds in 15 minutes Cures in 3 hrs. Dries clear and cleans easily with water. Recommended set-up time is 5 minutes to allow adjustment of the joints dynamically (throughout the joining process). Slow set up is more safe strong enable better precision.
Which glue to use...if it works and you are happy with it..then that's what counts.
"starved" corners may turn weak, sometimes (certain woods, very porous) wood absorbed so much of the glue's moisture that there is too little left between the surfaces to make a strong bond. Pre-gluing very porous wood prevents this and easy to do.
Secure the joints with fasteners once clamps removed or anytime after., It is a double source of protection.
Underpinner v-nail, brads etc.. is a personal choice, (It doesn't really matters) the idea is to secure the joints.