Most manufacturers make what you seek. Choose, or let them choose, whatever has the features you like: muzzle threads, dbm, twist rate, integral rail, aftermarket support, etc. I like tikkas and rem 700 and clones for this. Keeps me away from the new wave of turkish imports, which seem to be really nice. I am particular about the rear of the bolt, but i somehow dont mind the plastic tikka shroud. I dislike the great savage 10/110 for this reason, though I cannot rationally explain why; they are great.
Starting with LA/SA, 30-06/308, is that satisfactory for your/their needs? They are certainly ample. But a little vanilla for some. Faster is flatter and simpler in the field for holdover. I load for/shoot a lot of different rounds, like over 40, but in the field I almost always use something just under 3000 fps muzzle speed. That said, I have more 308s than any other round. I like conventional/cup n core bullets because they are cheap and they perform at the speeds I have found work best for killing/meat preservation.
280, 280ai, 270, 25-06 all perform for your game limits. The 25 is a first order killer, but borders on too light because of the bullet possibilities due to slow twist. My opinion of course. I use 100gr game kings at 3300, breaking my general rule of 3000 max muzzle speed. It does bruise a lot, but it kills like lightning. The 280ai with 162 sst or eldm is great on the other end of the 25-06. Just a but faster than the ol 30-06, and just a little flatter shooting. Over the 30 bore in that case, look to the Whelen. But it limits range significantly and likely wont be a favorite.
7-08, 260, the Creeds, Souper, 243 are all faster and flatter than the 308. The extreme of the 243 makes it my personal minimum for big game of all types up to 400#. It has worked, but many find it light. You have a different outcome with 7-08 or .26 rounds. The Creedmoor is useful and bests many similar rounds because long bullets work in the 1:8 twist. This is why it has nearly replaced the 25-06. It isnt faster, but it kills farther. As an aside, the 25 Souper is probably dead and will be revived as the 25 Creed which is just fine with me. Ditto the 260, which makes me just a bit sad. I respect Carmichael's writing and invention.
Now, for the others. The WSMs and WSSMs, the SAUMs and the PRCs and the like. I dont see some of them as options, and the others will be around a long time. Hornady's marketing and production and the down range performance of the PRCs will likely keep them valid as the 30-06 and 375 H&H have done; undeniable killing power and thousands upon thousands of successful hunts under them (but so it is with 30/30, yawn). I'm two seasons and half a dozen big game kills with an 8 twist 6.5/284. It is equal to the 6.5 PRC, but niche rather than available at the local farm and ranch or some gas stations. So marketing and production have made the PRCs more than their goofball (equal) counterparts, regardless of storied histories and novel shapes, etc. Not to mention fast twists in factory rifles and the many advantages/outcomes of that.
I wont discuss glass other than to say buy every feature you can possibly afford. Glass is forever, barrels are not.
My kids have started, or will start, big game hunting with a 243. I have several bullet favorites in that: 87 Hornady HPBT (harder than you think), 100 Hornady SPBT (as soft as you think it is), and 95 Nosler BT (ditto). The 87 must meet resistance to work, so shoulders must be shot. There, I said it.
My 15 year old took over my 280ai with 162 SST. Soft, super soft, but long enough to arrest expansion and penetrate like mad. Like a plastic tipped Partition, but cheaper and way sleeker. A true killer of the things, but possibly not for rear-on shots of elk, etc. The 162 ELDm can interchange with the SST.
My favorite 308 Win bullet is the Hornady 165 BTSP. It can shed the core, where the same bullet in flat base generally does not. Im ok with it, even on elk at 400. Soft helps the "little" 308 shoot above its diminutive weight class. But don't expect to hold on at extended range; the 308 isn't fast enough to kick hard nor shoot flat.
Factory ammo can be had to match the ammo combos I mention. Factory rifles too. But the guns you put a bunch of effort and thought into could be your favorites. But then a bolt '06 could too and it would save you/them thousands in other guns, safes, insurance, more optics, dies, brass….
So, after all that: Tikka T3 variant in 30-06 or 308. Done. Go smaller diameter if you want flatter shooting and or less recoil.