I can't stress enough to avoid Mardi Gras! It overlapped President's Day weekend one year. I wish I had I known!
As far as rooms, my son was 7 the first time we went, we did a Cars Suite at AoA. He LOVED everything about it. He also wore out the Cars DVD, so I expected he would love it. He is now 11 and we went back to visit AoA in January (we were staying at CBR), he just wanted to see all the cars again.
We love the moderate resorts. Great pools, they have slides, which my son loves. POFQ is great, it is a small moderate resort. Single bus stop, you aren't walking forever inside your resort. We've stayed there twice. We just stayed at CBR - the Skyliner was a game changer. But HS was our priority so it made sense for us. Worst part, the buses. Believe everything you read about the horrible buses at CBR. If MK and AK are park priorities, look at a different resort. If EPCOT and HS are a priority, then CBR is the way to go because of the Skyliner.
Weather, we've been lucky the last five years in January (MLK Weekend), and one February trip (President's Day Weekend), my son was able to swim on every trip. You will have more consistent warm weather in September or October, or early May. (in May watch out for a huge cheer competition, i think it is usually the second weekend!)
Have fun planning!