I am here on the N. Ill/Wis border, and can say that coyotes are an issue this time of year. There are litters which are in need of food, activity will be high.
Poison is illegal...get caught and your financially ruined.
As far as a cocealed cary permit, don't bother here in Illinois. If you want to take a class head to Wis, CC classes held every week.
A shotgun or .22 mag or better is where you want to start for coyotes.
A LGD dog will work wonders in keeping the coyotes away.
A firearm safe is not too expensive and can be used for not only securing your weapons but also for keeping other items safe.
There are numerous sportsman clubs in our area. Also firing ranges which offer firearm safety classes.
Once you get a valid FOID card you can take the rifle to the range and learn there, in a controlled enviornment.
If you have poultry, it is a matter of time before you will have to dispatch a preditor, you need to be familiar and confident with the weapon you purchase, before attempting to use it.
It seems like a long process, but it is better to have the weapon and know how to use it.
Good Luck