What is your rifle and caliber of choice for hunting medium to large game?

I've always been partial to my Weatherby Vanguard 30-06 with Nikon optics but I'm looking to change things up this year. I love my Savage 110 but I've only shot it once and I've heard great things about the Tikka T3. Also, I've never been a Remington fan, I've had 700 variants and the woodsmaster and it didn't quite do it for me.

An old 30.-30. Marlin. It has always been the go to gun for me here in West Virginia.
Iron sights.
It will take anything from bear to chipmunks.

I can only guess that this much be a question based on personal preference. I don't hunt elk (although my state has them--Kentucky). My two favorite rifles are a Marlin 336 in .35 Remington and a Marlin 1894 in .44 Magnum. The 336 has a Nikon 3X - 9X, while the 1894 has a Leupold 1X - 4X.

I've never seen much reason to own a belted-magnum.

I use a river #77 in 270 with a Nikon scope.

My Bergara B14 HMR in .308. It is light enough, far too accurate, and capable of taking any game in the western hemisphere.

Great question… Any 30 caliber will do.

If you mean medium game like a coyote or small deer up to large game like bear and moose then I would stay with the 30-06. You can use a 140 to 150 grain bullet for the smaller game and go with the 220 to 220 grain bullets for the larger game. I have several different makes and models of 30-06, what I look for is dependability, something that isn't affected by weather change, and will shoot consistently year after year. This being a singular preference like everyone else I like the Ruger M77 rifles; topped with Leupold or Nikon optics they always perform for me.

Been using 30-06 for deer and elk since 1973, no need to change that BUT 7mm RM, 270, 308 Win are all close enough to it. If I had a need for a lever gun might get a Browning BLR in 348 Win or 35 Whelen as an elk thumper. A nice thing about lever guns is they normally match eyesight limits, so they balance out well; the BLR is on par with many bolt rifles for accuracy which is a bonus. Once I started to load my own ammo it became pretty obvious that the bullet terminal performance available today trumps going to heavier caliber or even bullet weights. I would trust my 30-06 with a 165 Nosler Accu-Bond or the 300 WSM with a 165 Barnes TSX as much as many others would with a 338 Mag or similar/heavier.
I started hunting with my dad's Rem 725 BDL Custom, thus a 700 doesn't represent as much to me as others, plus I can recommend as good or better rifles at every price point. I prefer my Browning A-Bolts for features and I get sub-MOA accuracy with my loads. I've shot my friend's CZ 550 Safari 375 H&H, same as a BRNO basically, and I prefer CZ over the Ruger 77 but that is just personal choice, Ruger has done great work on the 77's trigger group over the past few years. The Vanguard Series II is about the best value for accuracy per dollar spent, the Ruger and Savage entry-level American and Axis II are great values too. I like the Tikka T3, has a super smooth bolt cycle and Sako barrel, haven't had much exposure to the Bergara rifles yet, they come in with good press and the fit and finish is there. I don't need a Nosler or the more boutique rifles, as long as I can put a good bullet where it needs to go I'm happy. I only have the 300 WSM because it's a gift, and my son uses the 30-06 now, but even with the slightly better MPBR the WSM has I'd not suggest it over a 30-06 or 7mm Rem Mag; which is what I see most in the field by a wide margin over 300 mags and 338s. IF I had to pick a "deer" rifle for out west shooting then it's hard to not pick 270, it gets elk with a good bullet too, but if I had to hunt antelope then a 270 Weatherby Mag might be tempting, or the 270 WSM.
Edit: Just to add, the Savage 110 series is a good rifle, has many converts and fans and I'll not/can't say anything negative about them, but the ergonomics and feel just aren't right for me.
EDIT: If you were looking for a coyote/varmint rifle then 223 or 22-250 are great options. The 243 Win is a threshold deer, antelope, varmint cartridge depending on bullet weights and design. A 90 or 95 grain Nosler Ballistic Tip is a bit too frangible for my personal taste, Accu-Bond or Combined Technology or Winchester XP3 type performance, or Federal Fusion is where I'd look for factory ammo on game. For yotes I'm using V-Max bullets from Hornady. 243 is still light for deer if you don't get an angle into the boiler room; there just isn't much extra mass to travel through too much tissue. Too frangible of bullet can cause meat loss if it over expands also.

I have always liked Remington 700's. I have Ruger's, Weatherby's and Sako's as well as other makes but I feel the most confident with a 700.
Just my preference and have had good luck with them. As far as caliber I use many different ones depending on the location I'm hunting.

I started shooting in 1964, first rifle Marlin 30-30 lever, IMHO the best general purpose rifle on the planet.
First handgun Remington .17 match target, followed by Colt woodsman .22LR
Current hunting, a surplus Steyr SSG69 7.62X51 but shoot Winchester .308, I shoot match with this also, the nighforce 25x scope cost far more than the gun so swaps to a current handgun Remington XP100 in 22-250, both hunting and match.
I can easily take down elk to 1200 yards with either, done that.
Your question is much personal choice, the 80s production Wetherby with cold forged barrel in any .30 is going to be very hard to top, 30-06 or .300 mag will drop anything you will hunt at long range. Excellent gun.
I do very little hunting the last couple decades, I do a LOT of range shooting and little match, even slacking on that, shooting is a perishable skill and see a little rust forming, still, two rounds one will go through the end of a pea soup can at my 800 yard range.
Best I can say is gun and caliber preference is like a pair of good fitting boots, you just have to try them on and go with the best fit.
Guns I wish I'd kept are the .22 woodsman and Gov. 45-70. I have a few other rifles and handguns for home and carry defense, happy with my old school stuff.

.30 caliber is good for the size… Ok, jot that down.(.30 caliber)
Where are we going hunting? (Like in location)
I live in Texas so invite me on a hunting expedition in Texas.
Again, where are we going in Texas and what are we hunting?
The panhandle?! To hunt deer! Well, I will take a scoped rifle and proper round for long distance shots like a .300 Weatherby magnum or just a .300 WinMag for the deer in the panhandle.
Oh, you changed you mind? East Texas for whitetail? Still .30 caliber but lever action .30-30 without scope will do for average 60-75 yard shots. Take in a little hog eradication if we don't see any deer. Still .30 caliber and lever action.
Central Texas for deer… Still .30 caliber but maybe a little better scope to ID animals to sort game from non game and not so long range(3-9x40 is good enough). Deer come in all sizes in the heart of Texas… From Père David's deer to those little chital or axis deer. 75 lb to 375 lb animal is a pretty wide range so your group of strong arms are more concern than caliber if you harvest one of those giant Père David's.
Maybe we'll go out West Texas some day… Another time, thank you (still .30 caliber).
The rifle? I can adapt to any rifle sold on today's market. I'm not a complainer about whether or not it fits my hand perfectly, heavy or light trigger pull, have to bend my neck too much, or the cheek pad is too this or that. If the rifle will shoot… I can shoot it… If it won't shoot I can fix it and then shoot it.
I do pull out my Carl Gustaf Swedish Mauser 6.5x55/NF4-14x50 for coyote because I don't have to leave the house.
Still .30 cal will do just fine in something else including .30 cal Mosin Nagant.