I really like coil spring traps. I've done well with duke pro series and bridger and MB traps. I don't personally use 4-coils and have actually cut all my 4-coils back to 2 coil. I trap after deer season, mostly dirthole sets for coyote and bobcat (you'll catch coons and possums too) and dogproofs for coons. I generally don't trap when the ground is frozen.
Dirthole sets are easy enough to make. Drag a log or rock to your site, use a cordless drill with a long auger bit on it to drill a hole at an angle back under the rock. Or log. Or tree.
You can hang a single feather above a set, so that it moves in the wind, to target bobcats. They'll notice and investigate the movement and find the bait in the set. Hard to believe that works until it does (see pics below - notice the crow feather). I use basically any form of red meat for bait. I've bought canned beaver baits but squirrel hides/guts and deer scraps have worked well for me. I use sardines for coons in dogproofs. The *best* advice I would give a new trapper is this: run trail cameras on likely travel routes. Any natural funnel where you see deer traveling is a likely spot. Coyotes and bobcats will run those trails also. Find areas that they naturally travel - you won't likely nail this in the first year - and then set your traps (again, a basic dirthole set is fine) 10-20' upwind of those trails. I've found that I can put the traps in the edge of thick stuff where deer don't/won't walk and avoid catching deer for the most part. If a coyote smells your set, he'll investigate.
Because I only trap in winter, I will often move logs and rocks when I happen to be around during deer season. Like if I need to go to a trap site to retrieve a deer or move a deer stand, I'll do double duty and move a log or rock and let it sit for a week or month before making a set from it.
Nothing has improved my trapping more than paying attention to my trail cameras and putting sets where animals will find them. I've made some beautiful sets that I was really proud of that never caught a thing because they were in dumb spots.
Buy a bunch of wolf fang type anchors. It's amazing how well they hold if set properly.
You need:
A half dozen traps. This stuff takes time; if you're a farmer with winter free time, you might run dozens of traps, but most people can't spare the time.
At least a dozen wolf fang anchors and a driver rod and hammer. Or get one of those long t-handle steel probe rods. That's what I use to set anchors.
Buy at least a dozen screw-type chain links to attach your traps to your anchors. Have a wrench because they'll rust up or get stuck and you won't be able to unscrew them with your bare hands.
Understand that anchors, once set in the ground, are pretty much there forever.
You can use chains or cables to wrap around a tree as an anchor, but I just use wolf fangs most of the time for dirtholes. Set the anchor, then attach the trap to it before you bury the anchor the last couple of inches, then set the trap right on top of the anchor site.
A suppressed .22lr is the ideal dispatch tool but I've made other things work.
You need a cordless drill and an auger bit to allow you to make your dirtholes
You need a small shovel, some gloves, maybe a garden trowel. Go on and dig up a 5 gallon bucket of good sandy dirt and keep it in the dry to use to bed traps.
Some sort of mat to work off of and mitigate the amount of scent you leave, is helpful. You'd better believe they'll smell you. Fortunately, smelling people is normal for them, where/when I trap.
Whether you need trap pans, waxed dirt, and things of that nature, depend a lot on weather. Here in the south I don't trap much when the ground is frozen but if you're further north, you should look into those things, but I can't really help you with them.
