For a 4wd truck it's probably not an issue, but I looked into the same thing for the wife's '16 4x4 Cherokee and they won't fit in the wheelwells (according to the manufacturer). So, that might be something to double-check just in case. As for what kind, I couldn't say. I grew up in the midwest where it snows in the winter, and I've never needed a set of chains. 4 wheel drive (or front wheel drive) will go a LONG way...IF you know how to drive. Personally, I'd skip the chains unless >80% of your driving will be rural.
Also carry:
jumper cables - The longer set you can find, the better. When the weather's nasty or depending how your vehicle is situated, the "jumper" might not be able to get too close to the "jumpee."
ice scrapers - Get a long-handled one with a brush on the other end to keep behind the seat a short/sturdy one for the glovebox. It's always nice to have options, and you can sometimes convince your passenger to get the side windows while you take care of the windshield.
Remote start - worth every penny if you can; I've thought a few times about moving back, and this was first on my to-do list if it happened.
Gloves in the glovebox - seems like a no-brainer, but you'd be surprised how many people don't. I generally keep 2 pair; one of the cheap "jersey" style brown gloves and a heavier, winter-type glove.
Warm blankets (at least 2) behind the seat (the green wool type work well) and a space blanket or two wouldn't hurt. If you're not normally a hat person, keep a stocking cap in there too; they're a Godsend when you need one.
Road flares - Full size - good for the obvious, but also good for starting damn near anything on fire if need be.
Throw some weight in the back of the truck during the winter: firewood is a good choice (can always burn/replace if need be). Or, befriend someone at the local Farm Supply store and have 'em get you an old tractor tire tube (that still holds air) and have them put an ample amount of calcium chloride in it. Tractors use it for weight in the tubes, and it won't freeze (just don't get it on your hands, or you'll find out real quick if you have any cuts or open sores...).
A QUALITY tow rope (not the ones with the pot metal hooks on the end). I like overkill, so I keep a large one behind the seat. Make sure you have solid recovery points front & rear on the truck; I much prefer d-rings (shackles) over hooks. And, just in case you didn't know (some folks don't), NEVER put a rope/chain around a hitch ball (youtube it if this is the first time you've heard this).
I'm sure there's a bunch more stuff that could come in handy, but I've never personally needed more than this (except for maybe a better jack than what came with the truck and a full-size spare tire).
-WRM