I am a "maximum" 100 yard hunter (might have even been me that posted that recently).
Since you didn't ask "what is best" but instead, what would you use I will take a crack at that one.
I have hunted Deer and Moose pretty much since I could hold/fire a rifle - so somewhat over 40 years now. I have hunted Moose in Northern Ontario and Newfoundland, and Deer in Eastern Ontario, so while some interior B.C./Alaska Moose are "bigger", these guys were "big enough" and Ontario Deer are somewhat larger than you find in the southern States or out west (save mulies).
Up where I hunt Moose (primarily) the Native hunters (Cree's) predominately use 30-30's - so while that is "enough", I don't know that it would be my first choice. I have used a 30-30 for deer (pushed by dogs) and it worked well for years, but ultimately settled on my 30.06 as my all round/general purpose/use it for everything gun - at least until now.
I just bought a 243 Win and it will become my new "deer gun".
While the ballistics suggest that I could also maybe/probably scrape by using it for Moose at 100 yards or less (and if you can't get within 100 yards of a Moose, at least where I hunt, you probably shouldn't be pulling the trigger on one) I personally won't use it.
I hunt rough terrain - lots of muskeg, bogs, swamps etc so if Bullwinkle doesn't go down "immediately" you might not be able to recover him (we travel in by train and literally get dropped off at the side of the tracks - no roads, no atv trails - so no atv's - no horses, nada - you have to get to him and get him out "on foot") - that really precludes any desire to track and recover - I need him DRT and you don't shoot unless where he will drop will leave him "recoverable".
Because of that I want the ability to shoot a little more than a 105 or 107 grain bullet - but not a whole lot more.
I am now in the market for a Moose rifle for my very disciplined, max 100 yard hunting style. I prefer to shoot Swift A-Frames at Moose (Nosler Partitions which I used for years are the "only" other option in my books - but after shooting them for a couple of decades I found the A-Frames just stay together a little better on Moose).
At sub-100 yards I personally consider 140-160 grains of A-Frame "enough, with a little margin" for Bullwinkle.
I can "launch them" with calibers in the 6.5 - 7mm "non-magnum" offerings currently on the market.
I'm becoming recoil sensitive so a 270 Win, probably in an auto-loader (Rem 750/Browning BAR) is the "MOST" I would want to pull the trigger on. It would be "more than enough" gun for what you have listed. But still would not be my first choice.
I would suggest, with disciplined, sub-100 yard shots, passing on "iffy" or quartering towards shots (at least for Moose - big bones cover the vitals) you would have "enough gun" with a 6.5 Creedmoor, 6.5 Sweede, 260 Rem or a 7mm-08 Rem. All could be loaded with at least a 140 grain A-Frame or Partition which will absolutely get the job done.
They could also be loaded a little differently for Deer and none of them would kick even half as hard as a 30.06.
So if you don't "need" a 300 mag to feel confident enough to pull the trigger, the terminal ballistics of any of those four calibers, that all have a reasonable choice of ammunition available "off the shelf" (if you don't reload), are more than enough gun for what you want to hunt.
(my new "moose gun" will either be the 6.5 Creed or 7mm-08 - just have to try the models "on for size" and decide from there - but it will be one or the other and I won't hesitate one iota when a big bull comes into the crosshairs)
At 100 yards or less a fixed 4 power scope is "enough" - I tend to use 3-9X40 or 42mm scopes because they are kinda the "standard" and you can spend as little or as much as you want. I do tend to leave them dialed to 4 or 5 X for short range hunting - at 9X on a Deer standing 35 yards away, you can literally count the hairs on their shoulder just before you drop him like he was pole-axed