Sorry to hear about your recent difficulties. The installation of a water heater is not very difficult and there are installation manuals provided with the units that explain the venting requirements. Without knowing you abilities, I cannot say how easy it would be for you but it is the easier item on the list to do yourself.
The furnace and AC are a different story. Installation is more than hooking pieces together. A technician uses special tools and knowledge to verify proper performance. The AC cannot be installed by a homeowner. The soldering of the lines, charging, and evacuating ect. Is very specialized and should only be done professionally! The selection of the equipment size and features for your application can affect the performance and efficiency. The installation varies greatly in each home and there may be special circumstances that you cannot determine. A skilled technician can help you make all of these decisions and save you a lot of time and money. I would hesitate picking out any equipment online yet. Without knowing what your needs are you may end up with equipment that is too big or too small for your home and are stuck selling it for half of what you paid.
Get some estimates. Have contractors actually look at the existing ductwork and do load calcs. The ductwork and venting specifics can change the cost dramatically. If you can determine the right equipment needed and find a contractor willing to match an online price or install the equipment you purchased that might save you some money.
I have to admit I have done this myself. Many years ago before becoming a home inspector, I did this on my home and a few other investment properties. I have a family member who is a very experienced HVAC tech. he got me the equipment wholesale price and we installed it on the weekend. It seemed very simple at first…the furnace itself was simple but the ductwork in most homes is done so poorly it can cause many problems. It is much more technical than most people realize and best left to the professionals. The wholesale prices are usually about half of the list price the contractors show you. There is room for negotiation and if you find the right installer, they may be willing install the equipment you purchased.
I am the type of person who does everything myself. it is one of my many interests to learn how to do something and then complete it successfully. I have done this out of financial necessity for most of my life and have learned that sometimes it is best to just let someone else take care of it. The potential for a mistake in installation of HVAC systems is just too great.
Good luck with your projects.