They are hard plastic Jogging style strollers. I'm sure someone has a picture of them (I don't). There is almost no bag storage-- no basket and a small pouch along the back.
If you have a lot of bags, maybe consider renting a double.
I agree, a double might be the way to go for lots of bags. On the other hand, the tops of these strollers are pretty sturdy and I can put some not too heavy stuff on top, usually my backpack. Keep in mind all the WDW stores will ship your souvenirs/packages back to your room for you if you are staying on property. I've done this a few times and never been disappointed.
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