Hi, first post here, but thought I could help, as I do HVAC sales and have been in the field 13 years.
I have a similar climate here in southern Delaware and we are installing a hybrid system (heat pump with gas backup) in our house before winter. The heat pump should cost less to run in spring and fall than a gas furnace, and the gas furnace costs less to run in winter than a heat pump with electric backup. Of course this depends on utility rates but this is true for my area. You also have 2 sources of heat if something craps out.
I don't think you will be able to get equipment without an EPA card, and if you buy equipment online the manufacturer won't warranty it. So not do it yourself. Also make sure the warranty gets registered (usually online) or your warranty will be roughly cut in half.
You don't have to replace the furnace unless you are installing a higher efficiency air conditioning or heat pump system that requires a variable speed blower in the furnace. Another thing to consider is whether you will have to remove the furnace to replace the coil (if it's downflow and the furnace sits on the coil) and if you're paying to have some of the same work done twice when you replace the furnace.
We are going with an American Standard system, probably a 15 SEER heat pump and 2 stage 95% gas furnace. I prefer Trane/American Standard and Carrier/Bryant. We have been heating with wood for 2 winters because I was too cheap to buy oil, and will still probably burn wood, also am conservative on thermostat settings, so I don't see putting more money into higher efficiency.
Get 3 estimates, check duct, and make sure system size is reasonable for house. I can give you a ballpark price for my area if you give me the the current ac tonnage or model number.