This is a huge can of worms with all hunters.
Many seem to think that a very light, very frangible bullet like the 110 grain HP out of the .357 mag is just the ticket, but he has never hit the shoulder or tried to run a bullet up to the vitals while looking at a 3/4 away shot. The .357 is the very bottom, like the .223 in the having enough horsepower for deer. yes it will work. most of the time. But I have seen deer shot with soft 140 speer HP's that just blew all the meat off the shoulder and left the deer in agony but still running. I saw a LEO try 4 125 grain silvertips to put down a struggling road hit deer. Not one of them seemed to reach the needed areas to HUMANELY kill the deer.
That same .357 loaded with 158 softpoints would have made it much better for killing game. A .357 carbine loaded with 158's or 180's makes a darn fine brush hunting gun. light, fast handling and with enough penetration to punch thru when shot at a bad angle, the work fine up close.
The 30-30 or 35 remington lever makes a great gun for this type of hunting, but you are practiacally limited to about 150 yards. If you are hunting deep woods, with no logging clear cuts or roads or powerlines to sit on, they work just fine and have killed millions of deer. if you are hunting deep woods but are going to have that chance at the clear cut shot or the powerline shot, then consider moving up to a 7-08 257 308 class of cartridge.
Also be aware of the fact very very few deer drop dead at the shot. Almost all run a little ways. I have had them run a half mile with one lung still laying on the ground where it was shot out of the side of the deer. I have had them run 200 yards straight up hill into a thicket when the bullet has cut the heart and lungs right off at the aorta and pulmonary artery. If you are hunting really thick woods, having a bigger heavier bullet that just plows on thru and out the other side does make trailing them a lot easier, blood drains faster when you punch a hole and a vent into the deer. I have an uncle who always hunting the really really thick stuff of the finger lakes region of NYS and in Penn. He always used the .35 remington because the 200 grainers always left the body. two holes, twice as much blood. He claimed to have never lost a deer he shot with that gun. If you look around now, you can probably find a nice marlin or winchester 94 for not a lot of money right now. I was just looking at a Marlin 336 A rifle at the shop for $175 that has the longer barrel but it is a nice gun. Add a peep sight or a 1-4 x scope and that is all you should need.