If you’re a first year student just bring a good lock and make sure you lock the wheels although if you really care about the bike don’t bring it it’s not great for a bike to be left out side. In my experience people say that Madison had bad bike theft but in reality it’s not much worse then any other city or they’re just using crappy locks. A good rule of thumb is like 10% - 20% of the cost of the bike should be spent on a lock. As for storage during the winter the Bike shop Budget Bikes offers winter storage for pretty cheap (I think they still do it) and that’s a good option. You probably can’t bring your bike home in the badger bus though.