I did a lot of trapping 20-30 years ago. I also trapped muskrats extensively a few different years since when prices were up. I have recreationally trapped beaver along the way to procure raw material for getting some garments made, but I find beaver to be a bit labor intensive for my taste to be financially viable unless prices are way up which seems unlikely.
Basic gear: Muskrat are easy. There are 2 basic traps that one could consider "bread and butter." The #1 longspring and the #110 "connibear" or generic body grip. I actually prefer the Sleepy Creek brand 1 1/2 longspring as it has more weight for drowning and will hold a raccoon, but the #1 is a longtime standby for rat trapping and will work fine. Buy quality traps here, sleepy creek are the best, and cost the most. They are more durable, reliable, and weigh more for drowning. The #110 ( I use cheap Duke brand) is another all purpose "kill" trap that does not require drowning and is versatile for various sets...more on that to follow. I've found no need to buy the higher quality with these. When you add mink and raccoon into the mix, a few specialty traps come into play. The #11 longspring (2x #1 springs), the #1 coilspring, and the #1 1/2 coilspring (raccoon specific, but will take mink and muskrat). For beaver, the #280 and #330 bodygrip are your go-to. I'd avoid footholds and drowning locks as an amateur for beaver. Drowning locks: You should have some of these for mink-specific sets. Bodygrip setter: You'll need this for the beaver traps. Swivels: Your quality coilsprings and #11s will have these as factory standards. If you go cheap, you'll have to retrofit. Rebar stakes: You'll need some of these for shallow water bank sets for raccoon, mink and muskrat. Not needed to hold a rat, but the others are commonly encountered here, so firmly staking your trap is a must. You can buy pre-made or make your own. Wire...I usually use high tensile steel fence wire. This is for a "drowning leash" on your rat sets, and a drowning slide on bank sets for mink. A quality hatchet.
Muskrat sets: (beaver also at bottom).
House or feeder slide set. Find where they enter and leave the water on their feeder and den huts. Place your longspring trap just under the water here with a 4' wire to ensure they reach deep enough water to drown. Stake it firmly with a sapling pole.
Funnel or run set. Use your #110 bodygrip in a location where they are swimming through a constricted area. You'll find "trails" cut through the weeds between feeding and denning areas (you can also find them by bubble trails under clear ice), and also bank runs with an entrance under the water or entrances to primary den huts. Cover these trails with a 110 staked firmly to the bottom with sapling poles. You may need to push in some additional reeds or sticks to funnel them through the trap. Muskrat are very buoyant, and tend to swim near the surface. The top of your trap should nearly break the surface. Any submerged Beaver set is an upsized version of this. I like to wire a partially peeled red osier dogwood stick to the trigger as an added atractant for beaver.
Not really going to get into mink sets here, as it's late and I need my sleep, and mink trapping is a complicated business. Cut your teeth on rats, then get back to the mink.
