Brian Pearce with Handloader/Rifle Magazine has covered the 357 (as well as 45 Colt and 44 mag) out of lever action rifles. Of course most of his article was about handloads, but if memory serves 158 grain loads can hover around 1900- 2000 fps. The limitation becomes the bullet, as most 357s are designed to expand at revolver velocities. There are several that are suitable for a rifle, just pick wisely.
For the non-handloader the two you mention would be great and the Hornady 158 grain XTP would be a good choice I believe as well. Good velocity and a tough bullet. A 158 grain hardcore bullet should be plenty for deer too.
As far as range goes, the hotter 357 mag and 44 mag loads typically pick up enough velocity in rifle barrels that at 100 yards they roughly equal the velocity from a revolver at the muzzel. Trajectory is really the limiting factor then. You are probably looking at 125 yards max. If you really practice at longer range and wait for a good shot, the bullet will be up to the task at longer ranges than that. Again trajectory is the limiting factor here
Now, let me say this. Handload, handload, handload! The 357 is a perfect choice for a beginner. You can get about a zillion rounds out of 1lb of powder with the 357's small appetite. Also, bullets, good bullets, are quite reasonably priced, often come bulk packed, and there is a huge variety in that caliber . Further, you can probably buy a "starter" reloading kit from one of the major companies for the same price as 3-5 boxes of Buffalo Bore factory ammo. Finally, it is fun and tremendously satisfying. Touching off your own rounds adds to the wonder of spending time at the range, or taking game in the field. It also forces you to become all around more knowledgeable about shooting. OK, OK, Ill get off my soapbox now.
