Deer&Duck
The 160g weight is a great choice in the 7mm Mag it has been my choice for over 20 years and with the right bullet construction will cleanly take anything up to and including big bull elk.
In my own experience I found the Speer Grand Slam works wonderfully but gave up on Hornady 162BTSPs after taking my first elk. A few years back I experimented on an antelope with Barnes XLCs but was very disappointed and went back to the Grand Slams. My current load is a North Fork bonded bullet and I dont see that changing. My buddy shoots Speer Trophy Bonded which are very similar in design but dont have the circumferential grooves. I guess what Im suggesting is that, while the Sierra BTSPs may provide excellent accuracy IF you find the right load, their construction is less than optimum for larger game. If bonded bullets like the A-Frame, Trophy Bonded or North Fork are too pricey for your budget, I would strongly recommend using 160g Partitions or a relatively inexpensive bonded bullet like the Scirocco, Accubond or Interbond.
As to powders, the two 7mm Mags I have worked with (mine and my hunting buddys) both like IMR4831. This powder has consistently provided us with groups 1 or less with a variety of 160g bullets. (We both use CCI 250 primers; he uses Remington brass, I use Federal brass.) My North Fork loads use H4831SC which proved to be a happy combination with a 3-shot group of 0.266 center-to-center, or slightly less than one caliber.
YMMV
