I would take care of the furnace only, as it seems to be more of a necessary expense. A/C is just a nice-to-have, however most of the students will be renting in the winter months when they don't need A/C. They'll make due. Throw some paint on the cupboards to spruce them up, but don't waste too much money on a student rental place ... especially since they will likely see some serious abuse from students.
For these types of decisions, you really should develop a priority list, and a payback period analysis.
Btw, I agree with TRM. You're planning to make a big change to your life in the near term. This will add lots of joy, but also stress to your life. There's nothing like having money in the bank as an emergency fund to help reduce some of that stress.