I used to coyote hunt to supplement my income. The pay isn't great, but you can make money. I still hunt every year and use the money for my "gun fund".
If you are going to hunt them, 30-06 is way too much gun. I tried 223, 22-250, 220 Swift, 204 Ruger, and finally settled on the 17 Rem. The 22-250 and the Swift were great rounds, but could put one heck of a hole on the offside. The 17 Rem was a good mix of accuracy, range, and not destroying the fur. Downside is ammo availability and price. The 223 would be my next choice.
Also, you will need to learn how to call. It isn't hard, but it does take practice.
It is a fun way to make some money. Last year I took 23 coyotes, and averaged $10/each. That was for thick winter furs that were skinned, green, and frozen. Definitely find a buyer before you start, and find out how he wants them delivered. You can't set a price ahead of time as prices constantly change. But at least you will know what he prefers.
As for trapping, that can be an expensive venture to start. You could easily drop the same money as a new rifle on traps. At least with the rifle, if you decide you don't like it you can recoup most of the cost. Used traps don't fetch much money, unless you are the one trying to buy them. LOL