This summer my air conditioning was running pretty crappy. It would cool the main level but not the upstairs. The air also ran my electric bill sky high (much higher than normal for half the use.)

Winter weather is approaching here and I turned on the heat just to knock the chill out of the house. I turned it on last night but it didn't seem to work. I just thought I hadn't turned it up high enough and eventually turned it off. This morning it was super chilly. I turned the furnace on 80 degrees thinking it would warm the house up quickly. Still nothing. In fact, it seemed that cold air was blowing. I turned it back off.

Do you think it's time to replace? The furnace and air conditioning is the original equipment - right around 50 years old.

I received a quote about 6 months ago in anticipation of a furnace/air conditioning failure. Here are the options. Thoughts?

Furnaces:
Carrier 58UVB Performance 96 Gas Furnace
95% AFUE
Upflow only design
39 7/8 Inches Tall
Two stage gas valve
Premium Variable Speed Blower
Power Heat Igniter
Microprocessor based control
Limited Lifetime Warranty on Heat Exchanger
10 Year Parts Warranty
58HDX Comfort 95 Gas Furnace
95% AFUE
4 way multipoise furnace
Single stage gas valve
Multispeed Direct Drive PSC Blower
Silicone Nitride Igniter
Limited Lifetime Warranty on Heat Exchanger
10 Year Parts Warranty

Air Conditioners:
13 seer
Up to 11+ EER
1.5 to 5 ton capacity
Sound level as low as 74dba
Scroll Compressor
High and low pressure switches
Tough, baked on powder paint
Front seating service valves
Limited warranty: 10 year parts and compressor

14-16.5 seer
1.5 to 5 ton capacity
Sound level as low as 74dba
Scroll Compressor
Internal thermal overload
Solid, durable sheet metal construction
Dense wire coil guard standard
Baked on, complete outer coverage, powder paint applications
Limited warranty: 10 year parts and compressor

You need to find a good contractor who will calculate the heating and cooling loads for your house. I am confident your 50 year old equipment is oversized. You also should have the duct evaluated to determine if it needs any alterations.

What you have provided in my opinion is not a quote. The contractor needs to provide the model numbers of all equipment and the sizes. Once you have this information you can post it here for people to comment. Include your location and any information which you think is important about your house.

In the old house we also had the furnace replaced. I hated, hated, hated the new furnace. The furnace would turn on, the house would get warm, then the temperature would go down about 5-7 degrees before turning back on. The air was also super dry and we had never had that problem before. I don't want to make that mistake again.

Here's the actual information from the quote:
Remove and haul away old equipment. Install Carrier 110,000 BTU 80% efficient furnace with 35ft chimney liner.

Install a Carrier 3.5 ton 13 seer central air package with 25ft copper lineset, ac pad, a coil cond (can't figure out what he wrote) pump to pump to laundry. Elect (can't figure out what he wrote) and disconnect.

All permits, sheet metal, work, taxes, and cleanup included.

Warranties:
Furnace - 20 year heat exchanger
Parts - 10 year
Service & Labor - 2 year

Total Cost - $4890

Extras: air cleaner - $200
95% Carrier 100,000 BTU furnace $700 more

It seems that it makes more sense to get the 95% or 96% furnace but I really don't know.

The prices you quoted seem low. Is this the price after rebates? Did the quote include any model numbers? Carrier offers several models for furnaces and condensers. I suggest you avoid the Base model. This is what builders typically install.

I assume Michigan has cold winters. It would make sense to spend the extra money on a 95% efficiency furnace.

The problem you had in your other house sounds like a thermostat problem and not a furace issue. Are you getting a new thermostat? If so which model?

Are these the model numbers?
Carrier 58UVB Performance 96 Gas Furnace
Carrier 58HDX Comfort 95 Gas Furnace

It looks like the 95% Carrier 58HDX Comfort Gas Furnace with air conditioner is going to cost $5780. This furnace is one-stage.

The Carrier 58UVB Performance 96 Gas Furnace with air conditioner is going to cost $6380. This is a two stage furnace.

Does the heat pump just give me the option for heating with electricity or are there other uses?

Often a heatpump won't cost much extra than the A/C, and is a worthwhile upgrade if they cost isn't much extra. The time to consider doing this is when replacing an A/C. Heatpumps are often built better than their A/c counterparts with extra controls for protection.

If your electricity is reasonably priced (12-13 cents per KW hour or less), the heatpump can produce heat at competitive prices compared to gas when the outdoor temperatures are mild. If gas were to get expensive, you would have another option atleast.

I like to run the heatpump when its mild out, when you don't need the hot heat of gas.

I've dealt with the first company on many occasions and I've been happy with their service. The second company is a Costco contractor.

We propose to install one Lennox 2 stage High efficient furnace model G61MPV60-091.
This unit has a AFUE rating of 95% with a Life time warranty on the heat exchanger.
Price $3,800.00.

Option #2: To install one Lennox high efficient furance model G61MP60C-091. This unit has
a AFUE rating of 95% with a life time warranty on the heat exchanger and five years
on all parts.
Price $3,300.00.

The price to install a Lennox 13 SEER air conditioner model 13ACX-036 this unit is 13 SEER
rating. Price $2,400.00.

The price to install a Lennox Elite air conditioner model XC14-036 this unit has a 15.5
SEERrating. The compressor has a 10 year warranty.
Price $3,000.00

The price for a Lennox Merv 10 filter is $150.00.
The price for a Lennox Merv 16 filter is $250.00.

The price includes all labor, material, tax, taking away old equipment, 5 year warranty on
all parts and labor.
The unit must be serviced in years 2-5 for the labor warranty to be valid.