If you have or can borrow one use a 12 or 20 gauge shotgun with 2.75 inch #4 buckshot for the 12 ga ( 2.75 inch #3 buck for the 20 ga) Both are good coyote rounds and good for closer/moving coyotes. Just my 0.2 cents

AR15 / .223 is a much better option than any of those. I'm not a big fan of .17 HMR as a hunting rifle unless you're shooting squirrels.

A 223 Rem, 6 creed, or 6.5 Grendel, or the new 6mm ARC

It's quite hard to understand which one is the most comfortable without using them at least once

The 17 hmr will do the job out to 150 yards. Not the idea gun for the job. But if thats only thing u got. I wouldn't use a fmj. Hornady 20gr xtp hp ammo. That bullet will get the job done.. I carry a 17 hmr when i am going after bobcats. I use a Hornady 20gr xtp hp. I dont like using a 20 or 22 cal on bobcats.

My prefered one is Rem 700 using 223 ammo, but in general it depends on distance and your accuracy. You can use anything from .17 to 6 creed and it's all going to work, but might need some more accuracy with lower cals. My go to is Federal, but I've heard Fiocchi makes pretty good 223 ammo https://gritrsports.com/shooting/amm...ammo/223-ammo/ , got few boxes of Fiocchi, Hornady and Double tap(never tried those) from this store, gonna test which one my rifle prefers