For a family of 6, you can stay in suites (DVC resorts) or CL at AKL, BWI, WL and (I think) GF. There's also AoA and Coronado that can accommodate you. There's also the option to split your nuclear family into 2 rooms and stay at any resort.
Personally we love CL offerings AKL is our favourite resort - there's so much to see and do there, plus it's gorgeous! We're staying at BWI for our first time in sept, so can't say much for the actual resort, but we've been through there a few times and it is lovely, but not quite my preference. GF is gorgeous, it's a one day resort for me - DH would rather never step in there because of the perfume smell lol We're Canadian - living close tot he rockies, so WL isn't on my priority list, but it is nice, not posh (IMO) but nice. For Posh and outdoorsy, i'd say aim for AKL CL.
I like going in Sept Food & wine is lovely, also the halloween party if you're interested. The weather is still gorgeous, but not as hot. April is my second fav time - again, the weather is lovely, not too hot, but also hasn't hit rainy season yet. The Flower & Garden festival is my favourite!
As for ages and size of party - when we go with a wide range of people, we utilize rider swap a lot, make FP+ plans for the older kiddos most of the time. We do a lot of things together, but also split up as needed. We have phones to make plans on the fly while we're not together. Basically, we just know we won't do everything, instead we ask everyone what their top 2 rides/attractions are, and we make plans to accommodate those requests as best we can.