Carrier/Bryant and Amana/Goodman are pretty decent. Some of it depends on what AC coil you have (or will get). I assume the Trane comment is a joke, but they are good as well, but not their AC compressors. Most contractors will utilize one brand only. Bryant is the "economy" brand of Carrier as is Goodman for Amana. Same product in most cases, less warranty.

I have two Trane furnances w/ Amana AC units, givng the best of both worlds. High efficiency is all you can really put in by Code, and you really should get a permit, especially if you ever plan on selling the house.

As for the tankless water heaters, strongly recomend you pass. They are good for some applications, but their safeties in general are not enough yet and the cost will NEVER be returned even with a rebate. A high efficieny water heater (with a commercial tank) is a much better option financially and from an efficiency standpoint.