I have a MistKing. The starter system cost right around $100 plus 2 buckets. I would say (and would imagine a lot of others would agree) that the cost was worth every penny. Can a dripper with hand misting work? Absolutely. IMO the automated mister gives you the following advantages:
1. Routine. Chameleons thrive on a steady routine, and they definitely know when scheduled times for misting are. A steady routine I think lowers potential stress on an animal and makes them more comfortable.
2. Flexibility. You and your family can go away for a weekend, you can be out overnight, and your school/work schedule can change without worrying about who will spray your cham. Chams can go a day or two without food, no problem. They cannot go without water.
3. Environmental stability. A programmable misting system can be adjusted depending on the season to help maintain humidity levels. I add several more short mistings during the winter when the humidity in the Midwest drops to nothing.
4. Moisture control. Hand misting and drippers use a lot of water. Not a good or bad thing necessarily, it depends on if you have a drainage system in place. A mister can be tweaked to not soak your enclosure and let everything dry out between mistings.
5. Easier. It will be way easier on you and your parents! One less thing to have to do every day. I would also highly recommend putting your lights on a time. Make it easy on yourself.
I think a good automated misting system is a valuable investment for your chameleon's well being. Look into MistKing and AquaZamp systems. Don't cheap out on a less expensive system that might quit prematurely.
Do you have to have a mister? No.
Would it be a great investment? Absolutely.
Have fun and post some photos of your cham!