The live trap you mention is a good starter. Key isn't so much using great baits but making sets on good locations and making sets that attract and catch animals. Start out with your live trap, if it held a possum then I am assuming it is large enough to hold all of the small game animals you mention or seek. Set that trap near sign...for coon look for coon trails. Coon trails are the little coon highways that connect all of their basic needs in life such as food, shelter, cover, water, and so forth. Good coon locations generally have water such as a creek or pond, but not necessarily. Look mostly for good den or living areas such as very old, mature trees, old brush piles, old beaver bank dens, abandoned ground hog holes, and so forth. Old abandoned houses are also good den locations, as are barns, abandoned autombiles, etc. you get the picture. When I look for trails, start with the den locations and find the nearby food sources such as a crop field, or a creek or pond, then look for trails that just connect the dots if both areas were on a map. Coons are creatures of habit and use the same trails over and over so the trails usually are easy to locate, especially if well-used. Anyway, find some other sign such as tracks or droppings, and make sets near the freshest sign. Coons have a habit of using any old log, or flat area as a toilet. sets near coon toilets are great coon locations. Fencerows are another good place to check for coon trails.
Anywhere you catch coons you will get possums. For mink, stay a little closer to water but not necessarily always the case. I've caught mink in coyote sets quite a ways from water, but generally alwasy near either a fencerow that led to water or a brushpile near a pond or stream also. They like to stay close to cover when hunting away from water.
For bait in your live trap, use what you used for that possum...it obviously worked and will also be attractive to other animals too. cheap cat food also works as does a can of cheap sardines in oil. Fish or anything fish smelling is highly attrractive to coons, mink, and possums alike, and also cats, skunks, etc.
You can branch out and acquire some small game foothold traps such as #1 or #11 models, or 1.5 coils and on up in size to match your target game animals. Concepts are exactly the same though...make sets on location and near sign...the only difference is in the technique...other traps require staking, bedding, and something to hold the attractor (your bait or lure) such as a dirthole or a clump of grass...but again the key is just to make sets where you see animals already using the area...then concentrate on catching them at that location.
Good luck and welcome to trapping. There is a lot of hit and miss, and some learning to do, but that is part of the fun, too.
