in the old days, you would ask your neighbors and your friends for their "furnace guys" number and just go from there... rule of thumb was the rule of the day.
in the old days, You would also get three bids and take the middle one so as to get a good job done. today thats not really a good barometer of quality.
Today, there is a huge HCAV body of knowledge and all of that translates into the science of HVAC. The first place to start is to get a couple of things done before you hire a contractor.
1. blower door test. This will tell you how many leaks (and in some cases where) you have in your home. This number is important to number 2 below.
2. Manual J load calculation by a contractor not selling you an hvac system. This will show you what each and every room needs as far as air flow etc in order to keep each room and the house as a whole at the comfort levels you expect and the efficency of the unit you want!!! The idea is that size of the equipment is important for economy and comfort and this the science of making that selection.
3. static pressures, delta t and air flow (supply and return). of your current system, along with any notes you can make about rooms that are hot or cold. The idea here is to learn what is good or bad about your current system, so that any issues can be corrected by the new install.
Note that none of this is free and will cost some money, but better to spend it upfront and be an informed consumer then to pay for mistakes for the next 15 or so years.
I would also add that permits are a necessary part of this process, so check with your city/state and see what is needed. I did and found really interesting rules (no permit needed for like to like change out!!)...
so if you noticed, I didnt recomend any MFGR's... all of them have good equipment and all have had or do have bad designs. the real idea here is that no mater what the make (within reason), its the installation that makes the difference in economy and system longevity.
others will have more to add I am sure!!!!
just my two cents worth.