On our August 10 day trip, I think we had maybe 3 or 4 cheapies each and I ended up returning a few. I think they are the way to go because of size and convenience. Toting the bigger ones around, especially after you have used them. If you have the patience and inclunation to be really thrifty, I could refold the cheapie ones into ziplock sandwich bags. If you over buy, you can always return the extras. I also buy them in the same color, so our group is easier to keep track of.
Another thing to think of for the rain, is a stroller cover. Cover the stroller everytime you leave it unattended. We went on Buzz Lightyear our first rip and didnt head this warning and sure enough came off to find the stroller soaked.