Good suggestions so far. Yes, everyone seems to like their particular bus. Some of the guys that have posted have much experience in the school bus industry so you can trust what's been posted so far.
Lots of hills doesn't make a difference between flat nose or dognose. What really matters is engine/transmission. That's been covered well in prior posts.
My take: you don't want the type of bus listed on the CL ad. You've mentioned a couple of times about the heat and noise. The dognose type has the most heat in the drivers position because you're sitting a few inches in from the window and they just don't get the airflow transit style (flat nose) buses get. Noise wise they are quieter than front engine flat nose buses. You said that noise and heat is fairly minor, but if you know the difference it's not minor!
My favorite: Always a rear engine (RE) bus. Quiet and the least heat. Did I say quiet? Yes, MUCH quieter. And many of them have air ride in the back. Some shy away from them because they think the turning radius makes them less maneuverable. However, once you get used to it the maneuverability is a very minor thing. A RE bus travels well for long distance.
You talk about "SO Many buses!!" Yes, but not really. Here's a condensed list of RE buses, leaving out older (pre 199
buses to keep it as simple as possible:
International (Amtran) RE300: These are the big 81 passenger 40' buses with DT466E (or very rare DT530) engines and 3060 transmissions. Heavy duty chassis, air ride in back, high headroom. It's what I own and I love it. Great engine (cheapest parts that are widely available, good power) and transmission. The shorter version of these buses usually has the 444 engine which is a good engine but not the power you need for long trips.
Blue Bird: All American or TC2000. The All American is heavier duty than the TC but the engines/trans choices overlap. The big Cummins engines will have the same Allison 3060 transmission as the International. The Cummins also has the cheapest parts that are readily available. Great engine. They sometimes have air ride in the back but not always. Usually has the high headroom but not always.
Thomas: The newer ones have the cool looking front end like CaptSquid's avatar picture. Good bus but they seem to vary more with either a Cat engine or Cummins engines. Thomas for a while was owned by Mercedes so sometimes you'll see one with an expensive to maintain Mercedes engine in it. Basically, if you find a big Thomas with a Cummins engine (and the same 3060 trans) you're good to go. Also, they seem to vary with equipment more than Blue Bird or International. Some have air ride front and back, some regular spring suspension, some high headroom, some not.
There's more variation with the dognose buses but I think for your traveling purposes with 4 children an RE transit style is what you're looking for.