a polecat is a skunk.... name comes because you "wouldn't touch them with a 10 foot pole"
It's time to find a warm place for the winter... no babies... they are youngsters by now...
Never had a baby skunk, I dunno what noises they make in the nest.
They don't climb.... that is, high into trees. They will get into stuff at and near ground level.
I'd recommend that you get a single shot shot gun... 20 gauge... since you are likely to be less worried about the kick than with a 12 gauge, since you don't have one now. Single shots are disdained by the expensive hunting crowd... but, all it takes is one well placed shot... and a shotgun gives you an opportunity to be just a shade off and still "get your critter".
With a shotgun you can get a large range of shells. Thus, one gun does double duty. I'd use the following shot on these critters... all at close range of a few feet to 20 yards. Experience will let you get further range... but that is hunting... we are talking about shooting stuff here:
buckshot = rabid/unwanted dog, coyote, self defense (you say you don't have animal control in your area, so guess you may have to do it yourself)
Number 2 or 4 shot = coon, rabbit, possum, armadillo, goose, duck
number 6 = squirrel, snake
number 8 = dove, quail, snake
number 9 = skeet, clay pigeons, target practice, dove, quail
A single shot is easy to understand how to operate. My kids and many others started out with a single shot. I used one until I was an adult. It's not a toy, it's lethal. You could buy a new one, or get one at a pawn shop or used gun store. They are usually very reliable and the least expensive, most effective gun you can have.
I'm sure others will chime in with warnings, etc... but I know you are a smart and capable person and will understand what I'm saying above.