Well those 3 you have listed would all be good! We've stayed at all 3 of them.
So your biggest factor is a pool:
(1) BC ....honestly it's going to be hard to beat the BC pool as it's a very big pool with different sections to it. Some people don't like it because it's hard to keep track of their kids, but for your family that doesn't sound like it would be a factor (assuming 2 adults and 1 child). Even though we have 2 kids, they are twins and we never once had an issue keeping track of them as they stuck together. They LOVED that pool. Now they are 14 yrs old and still favor it over other pools.
(2) AKL has a nice pool, but definitely can't compare to BC.
(3) WL - I'm not current on what is happening with the new pool there but I thought I read there will not be a slide? Doesn't seem possible so I could be wrong.
Your other factor of convenient transportation:
(1) BC has walking paths to both Epcot and HS. Epcot is just minutes away, while HS can be a 15 minute walk or you can just take a boat to HS. My family always loved walking through Epcot to get the monorail to MK. That obviously is not the quickest way, but it was a fun way for us. You'd need a hopper ticket to do that. The only park we took a bus to was AK, so staying at BC was a big plus for us.
(2) WL is very close to MK to you'd have a quick bus ride and also could take a boat.
(3) AKL is only going to give you buses and the only park close by is AK.
QS breakfast......well the BC gets a bad rap for not having great QS. While I agree other resorts have a larger QS area with more variety, we've always found exactly what we want/need at BC QS for breakfast (breakfast sandwiches and mickey waffles). Check out the resort menus so you can compare:
http://allears.net/dining/menu/
I think your family of 3 would be comfortable in any of the 3 resorts. BC is a bit more "deluxe" feeling to us, but we really enjoyed the cozy (smaller) AKL room. WL was our least favorite in terms of comfort, but we are a family of 4 (with 2 teens) so that factors in to how we feel.
Awesome theming? All 3 of them! BUT it's hard to beat staying at AKL, especially through a kid's eyes. We just stayed there a couple months ago (savanna room) and it was pretty exciting to go on our balcony and see animals. There are many different parts of the resort where you can view the animals too. For us, though, we highly prefer resorts where we have other transportation options besides a bus, so that puts BC above your other 2 options.
Good luck choosing!