Go an idea for one I wanna try to build soon. What's a good choice of wood to use ?

Cypress will last awhile

most of the ones I have seen were just made from 3/8 or half inch plywood

there are several things you can do to make the plywood last btu before the current plywood shortage most traps were made from scraps and making them last a very long time wasn't the primary concern

I used one a cousin built in the late 70s he had made it in high-school shop and varnished it it was kept stored inside so it was still in very good shape decades later.

3/8 and a little poly resin and some 4 inch glass you could make a crazy strong light trap that was nearly impervious to weather resin is a little expensive at 50 a gallon

Advantech will last the longest without treating it.
But I'd still paint the outside

Choice wood is FREE WOOD
walnut pallets cut up but you have to drill the holes for the nails

Used to make them out of 3/4 inch thick pine boards.
Don't really matter what you make them out of, use what you got easily available.

Rough cut pine

I used my dad's potato crates when i was a kid trigger was string tied to one end to hold it up and looped over a limb back to the ground the lower portion of string was soaked in salt water and the bunnies chewed thru it dropping the crate this was in winter for snowshoes

Since you're in Mississippi you ought to be able to get cypress at a decent price. If you use plywood try to get HDO or MDO. It goes by the name sign board or form board as its used for outdoor signs or concrete forms. Advantech would be my next choice. If you use white wood or syp I would consider giving everything a soak in Cunap.

Old barn wood

I have old rabbit box traps from the PA game commission. not sure the history behind them trapping rabbits
also have 1 1/2 victor coil springs with PA game commission stamped on the bottom base plate