Minimum you will want.
Traps. MB550's are a great trap.
You will need some sort of staking system. I like the berkshire disposable cable stakes & stake driver. I do NOT like using rebar stakes.
Might want to get some cable and crimps or you can order cable stakes already made. & some quick links for attaching trap chain to cable stakes.
You will want something to dig trap beds. Im still using an old framing hammer.
You will want a sifter to sift dirt/peatmoss.
You will need some sort of pan cover. I use polyfill under the pan.
Pick your spot.
Dig your trap bed.
Drive anchor stake. & pull to set.
Set trap. Put polyfill under the pan.
Bed trap. Sift peatmoss over trap and carefully pack down.
Sift dirt over peatmoss to blend in.
Bait or lure depending on the type of set you are making. Can be commercially purchased or bait can be leftovers meat based food. I get a lot of refusals or rolling on the trap when I use lures.
So I almost exclusively use baits. Bacon grease, venison scraps, meat scraps, dead mouse, roadkill bird.... Figure if a dog or coyote will eat it, it would be a good bait.
Optional. (but nice to have)
Knee pad
Gloves
Peatmoss for bedding traps.
Wax Dirt & dry dirt.
Trap dye, paint, & wax.
Antifreeze or salt
trap setter tool.
Fancy digging hammer
Small trowel or dirt auger for digging dirt holes.
Pliers/cable cutter /wirecutters.