so I installed my own a couple years ago.
One thing about central heat and air - the HVAC companies typically don't let you install or even help install, probably since they want to make sure it's right since they'll be responsible for it. But to save money, it doesn't hurt to ask.
When contracting for my shop, I asked the guy who came out to size and bid the job if I could save some money by doing some of it myself. He went back and asked the owner, who said no.
Then when the owner came to measure and do the actual deign, including the ducts and plenum, he started looking around and asked if I built the shop myself. Told me if I installed the inside components, ran insulated ducts to diffusers, did the wiring, etc, it could save some money! I guess without seeing all that he had imagined future problems and conflict if someone installed and botched things. After seeing what I'd built he offered me $1100 discount - sure, might be fun!
The supplied all the pre-formed plenum, return filter housings, ducting, diffusers, rivets, sealant, insulation, tape, and even loaned a crimping tool. It took me a week or so but I cut and framed as needed, ran all the electrical, installed the plenum and inside unit, cut the holes in the ceiling, insulated and hung ducts, mounted diffusers in various rooms, mounted the outside unit on a concrete base, the inside controller, did all the electrical. Nothing was difficult. Their guy came back and soldered the copper, charged with coolant, connected the wiring, and tested the system.
This was a company I and friends had used before so they knew me - another company might not have done the same. Other bids I got (for the same Trane heat pump) were twice the cost. Pays to shop around. I found the most popular HVAC company in this area for residential were the most expensive. If you want to find a reliable and reasonable HVAC company, maybe do what I did and ask a good architect friend who designs and gets things built - they know all the contractors, structural engineers, material suppliers, regulations.
One thing I discovered about outdoor breakers - the big outside unit at the house unit at the house uses three. Even in a quality outside box gradual corrosion on the terminals can increase resistance, increase current draw, and evenutally destroy the breaker. I learned to I coat every terminal, inside and out, with dielectric grease to keep the moisture and air away. (available at any electrical supply house)
I do call the HVAC company every few years to inspect and test pressures and function both at the shop and and the unit at the house.
Of course, a window unit is trivial to install and a mini-split not that much more. The thing most of us can't do is the refrigerant charging and leak testing. A good friend installed his central heat/air system for house and garage
completely by himself - bought the charging and test tools and everything. But he was a lot smarter than me.
JKJ