IME the Speer HotCore bullets are superior to the "standard" Sierra bullets for most hunting - in .277, .308 and .358 calibers at least. They do not lose or slip their cores, and they penetrate more deeply than the Hornady and Sierra "standard" bullets at under 100 yards. The HotCores produce a slightly smaller mushroom, but this is not a negative IME.
If all your shots were over 250 yards then the Speer BT bullets might work better, they are designed for the lower impact velocities of long-range shots. Thus they expand quicker to a larger mushroom, but Speer does not recommend them for short range shots. Since some of your shots will be "up close", I'd recommend the HotCores over the other three types mentioned.