FIRST I would replace the heating unit, and get one that is more efficient to operate than a 20 yr old system. It is probably near the end of its life anyway, and you dont want any surprises when its way below 0 or 100 in the summer time. This is probably the most important thing to get done on your list.

SECOND if there is money left, replace the last 4 windows, or as many as you can. The new ones will be more efficient, and less maintenance, and will help lower heating and cooling bills. Adding on here, if you need new doors, and storm doors, this would be a good time to do them too.

Is there a reason to insulate garage ceiling? Room above it?? If that is the case, then that would be number 3 on the list. If no room above, and it is just a garage, then siding would be number 3 on the list. Since your climate is so cold, make sure you seal the exterior of your house well, or add insulation if more is needed, before the new siding goes on.

Have you had any preventative maintenance done on the furnace? I would do that first to make sure you make it through the winter. If the furnace is in good shape then I recommend you replace the windows and siding first. The reason is adding new windows and insulation will reduce the heating and cooling loads of the house. Once those improvements are done, the new HVAC system can be properly sized based on the new loads.

The proper way to size equipment is to do a load calculation. Unfortunately most contractors don't want to spend the time to do a proper load calculation. They base the sizing on rules of thumb which tend to over size the equipment. Over sized equipment cost more, uses more energy, and can potentially have a short life.

Thank you guys so much!!! We were thinking siding/windows would be first step because the furnace and AC were both serviced this year and work well (which is kind of a bummer because we have a home warranty!). This helps a lot!!

About a decade ago, we had an energy analysis of our then 115 year old home done by a NYSERDA approved company (New York State Energy Research and Development Authority). They recommended improving the insulation around the top of the foundation, putting some insulation in the ceiling of some rooms which were outside the basement envelope but with heated rooms above, and replacing our original gas-fired boiler. We did all of these things. They did not recommend replacing the original double-hung windows (they all had 50s-era storm windows), nor putting any insulation in the uninsulated walls. We already had insulated our attic.

Do you have any evidence that your heating system is not working well? You mention replacing the siding. With what would you replace it? If you want to do that (for aesthetic or other reasons), then that would be an opportunity to put (more) insulation in the walls, making them thicker. This would require modifying or replacing the windows, so it may be very expensive. Keep us posted!

I would insulate the garage ceiling first. (I live in central Wisconsin so know how brutal winter can be!)

Least expensive of the proposed. Easy to DIY. Can do it this winter or early spring. (You do not want to insulate the ceiling in the summer! If it is an attached garage, it will help keep the house a bit warmer. And, you will gain some above freezing winter workspace by running a space heater if you want to work out there.

Next priority would be the windows. Because window install could have an impact on siding choices, installation methods, etc.

Furnace and AC next.

Siding last because it's mostly aesthetic.

If you are redoing the siding at the very least you should add a paper barrier to reduce the air infiltration. Then consider adding the thickest rigid insulation that will work with your windows.

I would do the siding first. That's a weather integrity concern. I had Masonite siding on one of my rentals and found it to be, shall we say, less than optimally durable.

Windows next. Your house is new enough that it's unlikely to have been built with really solid, well-made windows, and old enough that those windows are probably degraded by now.

Then hvac system. Where you are, you probably don't even need air conditioning unless your house is atrocious for ventilation and fan cooling. If the furnace heat exchanger is still in good shape, it's not a safety issue. While I agree that improved efficiency is a good thing irrespective of fuel cost, natural gas is trending cheaper (for now). At 20 years old, your furnace is probably already at least 70% efficient anyway. I realize that many will disagree with me, but I would put this in the bottom third of any list.

Unless you work in the garage, insulating it more should be in dead last place. I wouldn't do it at all. Keeping your garage above freezing temperature can actually harm your car, because the warmer temperature accelerates road-salt corrosion.

Thank you everyone! This has given me a lot to consider! I really appreciate you taking the time/energy to answer!

From what I understand, the heat pump mentioned above probably would not be a good thing for your climate. My understanding is that they do not work well, for extreme cold, and you would need another heating source.

Replacing a natural gas furnace with a mini split in Nebraska? How does someone who lives in Nebraska get a Mass Save rebate?

No AC in northern Nebraska? in a area with the greatest variation between annual high and low temp extremes in the entire country? (according to WGN's Tom Skilling). The northern areas of the Great Plains have very brutal weather with extreme temps and lots of wind so priorities there differ from other areas.

My biggest concern would be comfort which leads me towards weather sealing, which would include windows and siding as needed. I am not a big fan of replacing windows unless they actually are a source of problems. Age alone does not equal need for replacement and costs for moderate cost replacement of large windows is quite high. Economic payback on window replacement is measured in decades, not years, unless the existing windows are truly falling apart. Correct flashing and wind sealing around windows is a very large part of the energy efficiency of the windows and installation quality is a major concern. Taking down interior trim and sealing all the gaps may be all that is necessary. Carefully done house wrap, with sealing all gaps in the house envelope will be a major portion of residing and choosing a good contractor is a must. Most customers are focused on the total cost and the final appearance but the long term payoff is in install quality.

Come Spring, get an "energy audit" from your electric provider, this audit is either free or at a very low cost. Make sure they are going to use a "blower door" to detect all areas of air leaks. My old (22 yrs) HVAC was costing me a fortune in propane. I found a competent contractor and together we decided that two systems were needed....and all new ductwork. O.M.G. The savings have been mind-blowing and, as a bonus, I have even heat throughout. Year previous to replacement cost of propane was $2700 for winter only, after replacement it was $900 for the whole year.

I would start with the heating unit.

I would have thought for best efficiency, then you’d want to replace windows and siding at the same time. Otherwise you’re getting replacement windows inside the existing frames. If you do siding and windows at the same time, you can get new framing integrated into the sheathing and housewrap.

Masonite is a terrible product especially when exposed to wet conditions but was quite prevalent many yrs ago in residential construction. I had it replaced several years ago with a reroof project. Recently in a remodel, I thought about the condition of my exterior doors. after examination, I found they were in very poor condition. I replaced then with energy efficient models and have noticed not only the improved comfort but also in gas/electric savings. deoending on age of your home, don't overlook your ext doors.

IMO

Ductless mini-splits are great units IF you can find a competent, trained installer. The so-called "installation certification" is rather worthless in all but large urban areas. This is an instance where experience counts.