I'm thinking of doing some trapping this fall/winter. My father in law's barn and hay shed get full of them, and some area landowners would like the population reduced.
Therefore I'm thinking of using a live trap in and around the barn area (cats) but have no idea what other type of trap to use, or how to use it. Any suggestions?

Well if your trapping in an area where pets could be a problem I would just stick to the live traps, but #2 foot traps work nicely for coons, just bait with peanut butter or fish,or try to find out what their eating and use that, there are many ways to set up foot traps mostly its a matter of setting the area up to put the animal in the most likely position to step on your nicely concealed trap covered up in a shallow hole as to make it even with the ground. just trial and error is the best way to learn

No.2 traps are way over kill for coon. A no.1 or 1.5 is enough for coon. If you use a no.2, the coons foot when it goes numb, he then has room to chew his foot off under the jawsand escape.I use No.1s and 1.5 on coons and the 1.5s on fox also. The 1.5s are strong enough to hold yotes but the jaw spread doesn't allow much room for error where he steps at for a good catch. 1.75 and up for yotes.

For in your barn Use live cage traps I would think. Not sure if a DP (dog Proof) trap would work on cats or not. I wouldn't think they would.

yea i use number 2s becouse their alot easier to get where i live and i never know when a yote might come by, i often use baits that appeal to different critters, sammy is right tho a 1.5 is plenty for coon

Ditto for yotes. Also if your state allows use of conis on land. The 160s will take care of coons fast. Here in Pa. we are not allowed to use on land. But water ways we can. 160s, There is no missing coons or other animal that pokes their heads thru the6 inch opening. But be careful where and how you set them on land. Not to many animals will live that puts their heads thru it.

I prefer a #1 coilspring or double longspring for water sets for coon. I prefer a 1.5 coil spring for land sets and would be reluctant to go with a 1.75 or #2 unless they were pretty old or I thought that there was some chance of a coyote or large fox stepping in it.