FIrst thing when hunting coyotes is that there is an exception for every rule! With that said, when you set up to call a coyote, try to sit in a spot that allows you to have the best vision of anything that ends up downwind of you. Coyotes will almost always end up downwind of the sound. If a coyote gets to the point that it can smell smoke form your cigarette, than it is obviosuly also downwind of your human scent, the smoke won't keep your scent from being detected. If you're not saving the pelt, then use the caliber that you shoot the best. Actually, sometimes larger cal. guns with heavy big game bullets won't do as much damage as one would think. The heavy bullets just won't expand as rapidly without heavy bone to hit.
I'd guess that more coyotes are still called today with hand calls compared to Ecalls. I'd suggest a couple of hand calls for starters. If you find that you truely do enjoy calling and want to get "deeper" into it, then you could spend the money for a high dollar Ecall. For starters, a jack or cottontail rabbit distress will do just fine.

A couple of "tips", try to get set up in a position that allows you to see well, expecially your downwind side. Try to get into the area undetected, and make sure any approaching coyote can't see your vehicle. Wear good camo, sit in shade if possible. Don't move around a lot while calling, don't be talking to your friend while entering the area that you're going to call to. Have fun. Don't sit in one spot calling for more than 30 minutes. Don't get frustrated for the lack of action. Expect the un-expected. Did I mention, Have fun!!