Same at my previous carrier. The PF did what was called an "arrival brief", which was a big picture thing. Something along the lines of "this going to be a coupled/hand flown ILS/VOR/LNAV/VNAV approach, plan on flying the published missed unless directed otherwise, we'll plan on exiting at (insert taxi way) to the gate via (insert taxi ways)", as well as any special considerations like runway contamination, fuel state if you might have to go missed and try another approach or just go to the alternate, etc. The PNF did the actual approach brief.

Also, we had two take off briefs. One at the gate before we pushed, another before take off in case there were any changes to the original brief.

My current job, PF does all the approach briefing, and just one take off brief.

It's on the plate, there should be no reason to omit it. Especially if operating in mountainous/obstacle laden areas. Also state fix that the MSA circle is based off of.