Were I you, I would pick up a .223 or a .204 Ruger for coyotes. You can get a Ruger American rifle in 223 for not a ridiculous amount of coin, and they tend to get good reports for accuracy.
If you can't afford an electronic call, get some hand calls. You'll want both regular and close range if you're going hand calls. If you use an electronic call, put it about 30 yds away from you so that when the critter comes in they are looking towards the call, where the sound is coming from, and not at you.
Once you start calling, BE READY! Coyotes tend to come in fast, and it sounds like you have lots of them. I always use a net facemask.
You might also want to watch some Randy Anderson coyote hunting videos on youtube. They are both instructional and motivational.
