My first elk was taken with 165 grain Federal Premium 308 Win. Might have been a Sierra bullet, but I do not remember. At about 175 yards. Hit poorly. Tough way to learn, but shot placement trumps just about anything else. Imagine there is a soccer ball, or maybe a basket ball, that has it's front edge between the animals front legs, in its chest. Gotta hit that ball - two lungs, heart and lung(s), blood vessels above the heart - all will have it down within 25 or 30 yards. Gotta hit that ball whether he is facing you, quartering toward or quartering away. An animal that is running straight away does not really give a new hunter a shot. If you are very cool, and very, very good shot, you might consider a neck shot, but must spend time to understand where that neck spine is - and you do not have very much to actually hit. Heart/lung shot is way higher percentage shot.
How far? Get your gear together. 8" or 10" paper plates stapled to a wood lathe. Make up half dozen. Place at random distances. Pick a target and take one shot - is there a hole in the plate - Yes or No - anywhere in that plate. If Yes, then you just showed you can hit the kill zone at that distance. If you missed, you just proved that you can not. Your max range, is the distance that you and your gear can put a hole in that dinner plate with the first shot - every time. If you do not have much trigger time, that might actually be not very far away.
By the way - that first elk of mine - I fired the first shot at about 7:45 AM or so - just barely into legal shooting time. I had been standing on a trail in the dark waiting for legal start time before starting a slow walk. I fired my second shot into back of its head about 10:30 AM - that was a long, long morning of tracking!! My first shot had hit rear end of the close side lung, then across the diaphram/liver. Bullet was under the hide on the far side - very nicely mushroomed. We ended up about 2 miles from where I fired first - easily 3 or 4 times that distance covered while tracking. I must have raised it 3 or 4 times - heard it get up and go, but could not see it - a few more steps and could see its bed in the snow. So much better to see them go down within sight, and stay there!!!
That would have been late September about 1982 or so - there used to be an across the counter antler-less elk (some years was either-### elk) in area south of Hudson Bay, Sask. So pretty much continuous mixed poplar and spruce bush with some open grassy meadows/swamps - all pretty flat, except ravines near creeks and small river. That first one of mine was a cow - 313 pounds carcass rolled into the cooler at the abattoir. Last time we were up there - 2002(?), there was active logging going on taking out all the spruce...