You could break it up yourself with a rented electric jackhammer or rented backhoe. Disposal would be the main problem. I would lean toward hiring a paving contractor for a complete job of destruction and disposal of the old then installation of the new.

By using a pry bar and a sledge hammer breaking standard 4 inch concrete isn't too difficult unless it has wire in it. Just use the pry bar, put tension on it lifting up and hit it with the sledge. Disposal is the big problem. With the cracks you mention I would guess there isn't any wire in it. Good luck.

You could resurface the driveway and save alot of removal headache. Look into a local contractor who does pool decks.(your local pool installers would know who to use.) This will save time and backaches for you. Cost might be high but by the time you break up the concrete, rent equipment, your labor, and finding a place to dump the concrete you will have spent just as much money doing it yourself. They can usually do the job in two days or less depending on square footage, you can also pick colors and styles.

GOOD LUCK!!!!!!!