At one time, Ducane made 75% or more of all gas furnaces sold in the US. You didn't see their name on anything, but they were the contract manufacturer for most all major brands except Lennox. So yeah, they definitely know how to make a gas furnace.
I've been out of the business for a dozen years, but during the 42 yrs my dad was in the contracting business, Lennox had a reputation for using almost 100% proprietary parts and the costs on any of their repair parts were outrageous as compared to similar component prices from other mfgrs. Dad had a strict policy that his company did not touch anything made by Lennox, for any reason. Where other mfgrs would sell parts at wholesale to any licensed contractor, Lennox would only sell to a Lennox dealer and the Lennox dealer would only sell at retail. So, if you chose to work on Lennox stuff as a non-dealer, you bought all parts for about 3X what they should've cost, and then marked them up the standard 50%. The customer felt like he was being screwed, and he was. But he was being screwed by Lennox and not by the repairer. Dad's solution to this was to tell anyone who had Lennox to call the Lennox dealer since they were the only ones with access to Lennox parts. IOW, if the customer is gonna feel screwed, let him keep all those happy thoughts within the Lennox family.
If Matt's info on Trane as now owned by Ingersoll Rand is correct, that's plenty of reason to avoid Trane. Ingersoll has cheapened and screwed up most everything else they've bought over the last 20 or so years, so there's not much to say they haven't done the same with Trane. FWIW, I actually thought York had bought Trane. If that turned out to be the case, then their stuff should still be fine. We used a fair bit of larger York equipment like centrifugal chillers and large air handlers over the years, and had no problems with quality or warranty support. A friend in the business sold York residential equipment for 20+ years, and had good luck with it too.
Carrier, Bryant, and Payne are the same basic equipment at 3 different price levels. Carrier will have the most baubles and bangles, and often the units with the very highest efficiency levels, but that all comes at a price. Reliability wise, I never saw any difference from one to the other. Carrier gave us a super high efficiency gas furnace and highest efficiency A/C unit when we built our shop in 89. The condensing unit croaked in 93 and I replaced it with a cheapo Payne that's now in its 20th year without ever being touched. Had to replace the fan wheel in the furnace about a year ago, and that's the only repair work done on it in 24 years.
Efficiency-wise, the best bang for the buck is usually the model one notch below the top for A/C equipment and for gas furnaces as well. You might pay an extra $300 to go from a 14 SEER to a 16, but the jump to an 18 might be an additional $1200 plus the $300. On gas furnaces, the percentage jump is even more pronounced. When we got out of the business in the late 90's, I could buy a 92% gas furnace for about $550, or a 97% one for about $1250. With markup, sales tax, etc, the 97% unit would cost the customer roughly an additional $1000. High gas prices make the higher efficiency models more attractive, but you're still looking at spending roughly $19,000 on gas before you hit the break even point and actually start saving money. If you consider the lost use of the initial $1000, the payback is even longer.
As others have said, the installer will have more influence on your satisfaction with the new system than the brand will. My own opinion is that Carrier and Bryant are hard to beat overall. Parts are available and reasonable. The quality of the sheet metal work on the enclosures, etc is head and shoulders above brands like Goodman. Overall build quality just looks better, without some of the sloppy solder joints, and wires pulled too tight that you see on the cheap ones. As a rough rule of thumb, the total cost of the job is going to be about 1/3 equipment and materials, 1/3 bare labor, and 1/3 overhead and profit. The labor cost to install one brand or the other is essentially the same, so a significant premium in the equipment cost doesn't make nearly so significant a cost increase in the total price of the job.