I really enjoy snaring beaver due to the simplicity and limited weight. I like 5/64" 7x7 cable but have had good luck with 3/32" as well. I have heard good things about 1/8" cable for reducing fur damage but have not tried it yet. I have used cam locks, reicharts, slim locks, gregerson locks, and sure locks. They all work but I think I am leaning towards the reichart as my go to lock. Its narrow profile and wide surface where it touches the beaver seems to be a great combination. For support I like plastic tubing for a "whammy" but have used the steel as well. I like to support with #9 or 10 gauge wire. A solid support is critical as the only thing that should move on the snare is the lock.
I like a short snare (around 32-36") with an end swivel. This gets the swivel as close to the beaver as possible. In shallow water I typically add an 8' 3/32" cable extension and either anchor to a tree or use a 2" Pogo. If I have good drowning depth I will put the snare on a slide wire. Sliding them really saves a good set location as a snared beaver on 8-10' of cable can really do some renovation to a wide area.
The last couple years I have gone to a smaller loop (about 8") set about four fingers from the bottom of the trail in a shallow water or dryland situation or about 1/3 of the loop below the surface of the water if they are swimming. My snares are loaded and close quickly. Setting this way gives me a good percentage of neck catches on adult beaver as the bottom of the loop is set to come in contact with the beavers chin or breast. Neck catches really reduce any fur damage. I do find a fair number of snares knocked down so my setting method is far from perfected.
If drowning, I feel comfortable using a larger loop set closer to the ground as fur damage from a body catch is minimized in a drowning situation. Just remember that the longer your snare is the more drowning depth you need...especially if you happen to hip catch one.
I only snare in non-drowning situation if I am on a 24 hour check or less. Even with swivels beaver can really abuse cable if there is any kind of entanglement in the area and your risk of loss and increased fur damage goes up the longer a beaver is in the snare.
As far as sets go...natural crossovers, narrow channels, baited sets, bank holes,castor mounds are all good places for snares. I just try to find locations that naturally lend to funneling beaver through a relatively narrow space. I don't mind adding some blocking but I don't get carried away. Most of my guiding is more of a suggestion than an obstruction.
Wish I had better pictures but here are some from a few years back.