I am planning to upgrade my group set to 11 speed 105 along with the bottom bracket. However, I have no idea what type of BB should I get and brand. If anyone could help me that would be great?
The trek archive is a bit light on B.B. detail but mentions an FSA Vero crankset.
Googling FSA Vero shows me images of a square taper which is pretty straightforward and means that the bottom bracket is going to be threaded. Most likely it is 68mm across the B.B. shell, which you should measure.
If it’s 68mm and you’re getting Shimano 105 cranks, just use any Shimano Hollowtech II (or compatible) road bottom bracket, which will have outboard cups for a 24mm spindle.