Personally, I wouldn't live in Madison. Prices are astronomical and you have to deal with liberal idiots 24/7.
Look into places like Verona, Fitchburg, Middleton, Waunakee, Sauk, Sun Prairie, Mt Horeb, DeForest, Windsor, Cross Plains, Oregon, cottage Grove. Depending on where in the city you will work, I would stay on that side of the city for living. You don't want to be on the beltline(hwy 12/18 from interstate out to Middleton area) during rush hour traffic...it's not nearly as bad as bigger cities...but it's slow pretty much every day and a joke if it snows.
You're not going to find squat for gun ranges or shops in Madison. Pretty much every gun shop in Madison moved out of town back when they had a ban on selling handguns in the city. Zero ranges that I know about.
There are gun shops is almost every smaller town around Madison though. Oregon has one that I drive by every day. There's a good indoor pistol range in Deerfield. I've been there a couple times. Gander Mountain is just North of town on the interstate and has an indoor shooting range as well.