Hey Skeets...
You're gonna drive the whole shooting community crazy.
When you ask these questions, you need to give more information.
When you ask "Which is better for coyotes, a 6mmBR or a 243 AI?"... there's really more to it than that.
For example, AI chambers are all over the place in headspace, since there are no "SAAMI" standards.
Someone we both know had TWO AIs built by one of the top gun makers, and BOTH gave head separations on the first firing,fire forming loads)... not a good thing. And what I hear some smiths think is their "crush", it makes the hair on the back of my neck stand up.
Also - in spite of all the hype, and some of the positive attributes of the AI cartridges, they have some drawbacks. They typically don't do
NOT feed well from repeaters without a lot of work on the rails, and most smiths that do AI's can't do the rails properly. So you wind up with a single shot.
Remington tried t make a repeater in 6mmBR, and threw in the towel - it is also a single shot cartridge.
When you ask this question,on 87 shooting websites

), you don't say what kind of shooting you plan to do.
Are you going to call and shoot, or set up and snipe, or are you going to do looooong range sniping. It makes a difference.
Coyotes are not small targets - at 500 yds, they are typically 4 to 5 minutes wide, so you don't need a benchrest grade rifle... but if you are going to need a second shot - you
WILL need a reliable feeding rifle.
There is the temptation to get extreme speciality calibers, like some bigassed case necked down to .224 and shooting 100 grain "
darts" at light speed.
While fascinating, they are not very practical for a guy that is new at rifles and new at handloading. Like sexy blond women, they look cool, and everyone says "Oooh aaah", but they can be real expensive to get, and a real pain in the ass to keep and maintain.
So tell us, what kind of shooting will you be doing, and what do you want from the rifle,performance wise)
But, what the hell, it's only money, right???
.