Yes, carry-on's are free!
Just remember to keep it within the size requirements. You also get one "personal item" for free (ie. purse, laptop bag, coat, etc.).
Yes, a small rolling suitcase would be considered the carry-on item. Just double check the size of it with the size limits for the airline. You can also take a personal item, I usually take my carry on suitcase & a large purse with my ipod, book, stuff I might want access to during the flight.