330 sized body grippers of any manufacturer. Beslile makes great traps but pricey. Bridger and Duke (although) both foreign made are solid traps for beginners and will get you going in the game for a moderate investment. If you plan on just trapping for a friend, a couple of 330's should do you well. If they are trap shy already, you may want to pick up a couple of footholds. If legal, the Bridger with an 8.5" jawspread can't be beat. Here in NY the maximum jaw spread in water can't exceed 7.25" jawspread. I have a lot of different traps and they're all pretty good to be honest. Sleepy Creek are excellent but they're no longer in business but there is still a lot of inventory at trappy supply houses. Anything from Minnesota Brand or the MB traps are excellent too but shoosh they are pricey and if you have thieves, you don't want to put high dollar traps out.
Trapping is highly regulated so be sure you check on the regs before you invest in some footholds. The 330 is a beaver specific trap that has a 10" x 10" jawspread... don't bother with anything less for beavers in terms of body gripper style traps (conibears). You can get into stakes and all that but trust me, use what is around the area if you can. Makes sure you do not use green stakes though as the beavers will chew them up and there goes your trap. The sets that I continue to use and recommend are ones that are simple and take minimal time. Basically, channel sets in water where they are going up to get food for the winter. Find a section where the channel will just cover your body gripper and set it in that channel for it to swim through on its way to go get trees and shrubs. Right now they are stockpiling for the winter so will see fresh cuttings and turds (they look like very large wood pellets about 3/4 to an inch in diameter and about 1.5-2.5 inches long and they just look like sawdust in a big pellet. Find these channels where they are swimming and set in them and you will get those beavers very quickly. Lastly, some states have regulations setting on or near the lodge or a dam or have minimum feet from the lodge or dam where you can set. Here in NY you have to be at least 15 feet from an active lodge. You cannot set in bank den holes but if you state allows it, those are money sets. They can be tricky to access sometimes with deep water pond type locations though. A "castor mound" set also is simple too and deadly right now, you just take a soccer ball sized of mud and goop from the creek, pond, lake, channel etc. and through it up right on the edge of the bank and then set a foothold with a drowning rig right in front of it. You can also do it with a body gripper but you'll have to "correl" the beaver into the body gripper a little bit. If they are trap shy for body grippers already because your buddy tried or had some kid try..... the beaver will be trap shy for that shape of the body gripper. That is when footholds really shine but you have to rig them to drowners in a minimum of 2ft. of water. Hopefully though they haven't been screwed around with a lot and you'll be able to set your body grippers and get some fur. Good luck!! For supplies, I like Sterling Fur out of OH, F&T Fur Harvesters, Kaatz Brothers, Sullivans Supply (Hal Sullivan's shop), there are tons. You can order directly from Duke if you pick up a Fur Fish and Game magazine or a Trappers Post or a Trapper & Predator Caller magazine you will find plenty of trapper supply houses in which to choose from. They are all good and you can comparison shop an all that but for what you need, get them ordered. If you're gonna use wire be sure to get trappers tie wire that is already annealed, regular wire is too brittle. Get 11guage for beaver, 16 for anything else. Better is aircraft aluminum cable in 3/32" size with swivels, you can use them for snaring and they make great trap anchoring systems too for water trapping and body gripper type sets. They usually come in 6ft. lengths pre made. They are a one time investment and you can use them over and over. You girth hitch them around a root, or a re-bar T stake or anything that will be difficult for the beaver to chew through and then you "S" hook the swivel end to the chain of your trap or I take my chains off and just "S" hook them to the trap spring. Finally, be sure to get some trap setting tongs for 330's too. These are a must for safety and because trust me, if you're buying brand new 330's, they are tough to set without setting tongs. It is even tougher to get a beaver out of the darn trap if you don't have tongs either. They are a must. I'm going to say it again. They are a must. Also, get yourself a trap safety for the 330. They clip on between the jaws once the trap is set and if you accidently hit the trigger when setting it in murkey water with a lot of chewed beaver sticks all around, you'll be glad you have the safety. There are also hooks on each spring of these traps to help you while setting them too but the trap safety is extra insurance and they're like $6 at the most. The spring hooks are the last thing you undo once you've set the trap but be sure you do it or you'll educate the beaver and the trap is ineffective with them still on. Finally, remember that the 330 conibear is a very very powerful body gripping trap. The new ones, especially the magnums, can break you arms if they go off on you and you will not be able to get it off by yourself. Which could be very dangerous if you are way back in. Also, if you're just starting out, be sure the have a buddy go with you.