I’ve owned a couple of levers, and shot a few more. IMHO, what caliber to get depends on what is useful where you live, what you are interested in, and what you can afford to feed. Which brand and model to get depends on preference and possibly purpose.
You can get levers that will run any .22 rimfire from short through long rifle loaded at the same time in the same tube. You can have .22 Magnum. Pistol calibers include pretty much any rimmed cartridge of the “cowboy” or frontier era up through the most modern bear stomping revolver rounds of today. Rifle rounds include the cross-over rounds of the frontier - .25-20, .32-20, .38-40, and .44-40, the .218 Bee, and on up to the largest rifle cartridges of the era including things like .38-55, .444 Marlin, .450 Marlin, and .45-70. Speaking of the .45-70, there’s a Marlin on display in the Tombstone history museum housed in the old courthouse that was used by a bear hunter in the late 1800s. It was discovered by his partially consumed remains when he failed to return from his last bear hunt - apparently, the old adage “Sometimes you get the bear, and sometimes it gets you” was true then as it is now.
In my family, people who prefer lever actions have mostly used and hunted with Winchester or Marlin .30-30s. One rifle in my wife’s family was a Winchester 64 in .30-30 an old cowboy bought at some point before WWII. All of his sons remember shooting it and hunting with it, and when he passed at 102, the rifle was the only firearm in his house, and still sat ready behind his bedroom door in the old ranch house. One of his sons has it now. Other family members had 1894s, but there was also a Savage 99 in .308 a WWII vet bought and used for elk and deer for decades.
The first rifle I ever saw was a Marlin 336 in .30-30 my dad had when I was a small boy. He kept it locked up in the old coal room. It got sold to pay the rent, IIRC, well before I would have ever been old enough or large enough to get to shoot it.
I’ve owned a Marlin 30AS (plain birch stocked 336) in .30-30 and now have a Marlin 1894 in .357. Where I live, the .30-30 is used for deer by some, but I rarely hear of success with it or stories where a hunter would have found success with it. Perhaps we don’t know how to hunt anymore, but hunters around here rarely find success at ranges the .30-30 and other traditional lever rifle calibers are usually considered useful for, so I sold mine when I realized I didn’t really enjoy shooting it and hadn’t found a use for it. My .357, on the other hand, is a very enjoyable rifle to shoot, a handy size and weight, and my very slightly build adult daughter will shoot anything I can load in it and be perfectly happy.
My dad owns a Henry Golden Boy, and everyone loves it, but who doesn’t love a .22 lever action with a slick action and tube full of fun?
I have fired a couple of .45-70s. They were tolerable for a few rounds, but not really something I’d spend a lot of time shooting. If I needed a bear stomper, I’d consider getting one. But I don’t, so my lever action “just to have one, and maybe hunt a little with it” rifle is the .357. I have a few .38 and .357 revolvers, so a lever in the same caliber is kind of cool because I can load for it with the same supplies on the same equipment, and carry one type of ammunition when hiking or backpacking. I’d probably be just as happy with a .44 Magnum or .45 Colt pairing.
Just my viewpoint on it: I’d get a .22 or a revolver caliber compatible with your favorite revolver. At shorter ranges, the revolver calibers from a lever action will be quite effective on deer, useful for small game with the right loads, and a lot more enjoyable to shoot more than the heavies. And a .22 will be fun for everyone and useful on smaller game or for pest control.