This is the kind of info I need! I've done some research and know the major pros and cons of each place but hoping to learn more from personal experience. My kid is a busy body and while a super awesome pool sounds great, trying to keep track of him in such a large space while he is still learning to swim is a little overwhelming. Would hate to stay there for their best feature and not be able to fully enjoy it. Maybe in a few years when he is a little more self sufficient and a practiced swimmer (he just turned 4).
Yes to renting DVC points. Yes to requesting a studio. Good to know about the BLT studios! Poly is making more and more sense.
Since it's DVC and we've had studios in all three locations, it is a no brainer to me to pick Polynesian. The studios there are the only ones I will ever stay in again due to us loving our space now lol. The studio at BCV is okay - not horrible, but can feel cramped when the bed is pulled out. As I said BLT is tiny. Two adults were in it the last time we had one and even then it felt tight for us. Polynesian are the largest and have the 2 bathing options (stand alone shower and bath/shower). They also have the Murphy bed which is so much nicer to deal with than the pull out couch. No need to make up a sofa bed, just pull the bed up and down.
I do think waiting a few years for BC pool is a good idea. We did after one trip we decided it was too much with really young ones. It's actually not our favorite pool since it is so crowded, so spread out and chairs are hard to come by (and literally so close you cannot get on them easily unless on the end).
BLT's pool is small and has a cute splash area for little kids. The walk to MK is okay but isn't very shaded and can feel a bit exposed if it's super sunny out. The ride to Epcot isn't bad, but the ride back is slightly annoying having to make all of those stops. The walk to the bus stop is a bit long, but not bad.
Polynesian's play area is better IMO and the pool is larger and a family favorite. Also the location I like. You can easily walk to the TTC to take the ferry or monorail wherever you want to go. So to get to MK we usually just take the ferry. To get to Epcot we walk to the TTC and skip the monorail ride around the resorts. The DVC rooms aren't far from the bus stop.
Beach Club is a nice walk to Epcot - very quick and the entrance to Epcot from there is nice. You can walk to/from DHS as well, but that is a hike sort of. We had issues with the buses our last trip getting to MK. The focus really seemed to be on AK. The resort is slightly removed from BC itself. easy walk to the marketplace but kind of far from the main pool anyway.
So saying all of this, that's why I would pick the Polynesian. Do the BC later when the pool will be easier. We waited a while for ours to get to be stronger swimmers. Polynesian has 2 pools and both are better suited for little ones learning to swim. BLT's pool is good for that too, but smaller.
Done rambling for now. We have obviously stayed at all 3 and love each for their own reasons