With this years fur prices,( $5 coyotes)
and you just starting out, I'd say go with the 7mm-08 you might have to sew
the fur some if you want to tan it for a trophy, but I'd hate to see you loose your first one, with a less then perfect head shot
with the 22 mag,not that you shouldn't use it, but even in the heart and lungs, they will still run a bit
Take the 22 mag on your second one.
Good luck