These are good questions. Here are some answers:

1. The mild NC winters and low electricity rates are ideal for a heat pump.
2. A SEER of 15-16 is fine for your climate and electricity rates.
3. In cold climates a 95% efficienty furnace is recommended. I don't know if you need such a high efficiency especially if you are getting a dual fuel system. It may be overkill.
4. Infinity is the top of the Carrier line. It tends to be pricey, but it in some situations it is worth the extra money in my opinion.
5. Heat pumps come in one or two stages. The Infinity furnace comes in three stages. A two stage AC/heat pump is great if you have high humidity in the summer.
6. The most crucial factor is properly sized equipment installed by a competent contractor. You can buy the best equipment but it may never operate correctly if it was not installed properly or the wrong size.

Why did you get a recommentation to replace your systems? How old are they and are there any problems?

A highest efficiency single stage heatpump around 15 seer will save you significant money on energy in the summer. It will also be very competitive to natural gas in the winter. It may even be cheaper than your 80% gas furance in most instances.

Having a 95% furance might be overkill in your climate especially with a heatpump but it the cost isn't much more than the 80% I would consider.

Finnicky

What size living area?

What general location in NC?

If nat gas, then var speed 95% two stg furnace with high eff AC.

Second option, high eff heat pump with 80% two stg VS furnace.

IMO

IMHO, a variable speed blower (furnace) is more important than a 2-stage compressor (HP or AC) for humidity control.

As a rule of thumb, going from 10 SEER to 15 SEER might save you nearly 20% on your electric. That would be around $100/yr for your summer usage.

With gas it will depend on installation costs of the 95% over the current 80% you have. Otherwise you could figure a 15% reduction in the gas bill upgrading to the 95% furnace. The increased costs might eat up a lot of the savings.

Things get a little murkier when you go hybrid.

I generally agree with above post.

Nat gas rates have remained constant and in some markets have actually declined. Did you know that Piedmont Nat Gas? While electric rates have continued to march upward.

In fact, based on OP's rates, there is really no leverage in a dual fuel system.

Want to comment on installation of high eff condensing furnaces. If furnace is located in a very accessible place and has access to a close exterior wall for venting waste gas and fresh air for combustion, then this cost should be relatively inconsequential and not really a big deal at all.

IMO