No I wouldn't provide for them

Go into the place armed, make all of them leave with your guns, and then take over the place. In a zombie apocalypse...I am only going to look out for my friends and family. Inmates are way down that list. Then, you could possibly set it up one day to be an outpost. You have all of that fence area so you can farm. Most of them have generators built in so all you need is fuel. You could set up some wind turbines or solar panels and become totally self sustained. Going up North is a good idea but food is scarce up there and it isn't always freezing. I also like the idea of going to a small island but the first thing I would go with is my prison plan.