Remember your carryon/personal item must fit under the seat to avoid charges. If it's going in the overhead bin, you will be charged. If they charge you at the gate for a carryon, it's $100. You may want to purchase a beverage once through security if you'll want one during your flight since sometimes it's cheaper than what spirit will charge you.
All that said, my parents still love spirit and even bought carryon suitcases to fit under the seats and avoid the overhead bin fees.
Make sure you read all the fees and try to buy whatever you know you will need ahead of time.
Just read some of the contract of carriage on their site as well and it says strollers do not count as a carryon item, so it seems you can gate check it at no charge. I would contact them directly though just to check.
Thanks for the link. My computer does not like the Spirit website. I have a hard time navigating it and It takes forever! I couldn't find it so I called spirit just to reconfirm.