I'll assume you are talking deer hunting since the game isn't stated.
To me, if you are only shooting out to 200 yards, the only reason to buy a magnum rifle is to shoot heavier bullets faster. You don't need at all to push a 140 grain bullet at 3200 fps for a 200 yard or less shot. You could make that shot with a 7/08 and 140 grain bullets so why deal with the extra rife weight and muzzle blast?
I would shoot 160/165 grain bullets for what you state. Trajectory will be negligible and penetration better than 140's.
When I bought my 7 mag in the late 70s I got 2 boxes of hornady frontier 154 g and they worked ok for me. When I started to load for it I tried 139 g and my friend and I couldn't find a load we liked. We ended up shooting 145 g speer hot cores with 62 g of 4350, very accurate and pretty fast. I don't take alot of long shots but have made afew and I know this load will do the job.