Hi Samantha,
The strollers in the parks are made out of a hard plastic material and are a "jogger" style. They do not have cup holders or baskets for storage underneath. They are, however, VERY easy to push, and can turn on a dime.
I'm a big fan of bringing your own stroller for a number of reasons. First, you'll save money on rental fees. Currently, a single stroller costs $15 per day and a double $31 per day. You'll save a bit if you get a "length of stay rental" for your trip. Secondly, I think strollers come in very handy in places outside the parks, including the airport, walking around your resort and going to and from the buses to the park entrances (the distance isn't huge, but it is a walk). Next, your kid(s) are probably comfortable in their stroller, and may be more inclined to stay inside it. Finally, and this gets to your question, Disney strollers don't come with all of the "bells and whistles" many at home models have, including cup holders for moms and tots, generous baskets and the ability to recline for an impromptu nap.
If you do decide to rent, click
HERE for up to date pricing and rental location information.
Have a wonderful trip!
Tanya