The on-bike chain cleaners work pretty well - I use the Park Tools version. I've used a citrus degreaser, but it's pretty pricey. I went down to x-mart and found a gallon of degreaser (purple something) for about $4. Kerosene works well too.
Suggestion #2: Go to the local dollar store and buy a spray bottle and fill it with your favorite degreaser (again, purple stuff works fine) and liberally coat your drivetrain and chain. Let it sit a few minutes. Now take a bucket of warm water with Dawn dishwashing liquid and clean your bike top to bottom. Use a separate toilet cleaning brush to scrub the chain and drivetrain. Rinse gently with a hose. Your bike, chain and drivetrain should sparkle nicely.
Allow chain to dry before using your favorite lube. There are many opinions on the Forums on this subject. You may want to do a search to read previous threads.
A chain tool is a necessity, and learning how to break a chain and reconnect it should be one of the first things you learn - after repairing a flat tire. However, IMO the reconnecting pins on Shimano chains are the weak links, so I don't like to break chains once they're on. Which brings me to SRAM chains with PowerLinks. They make chain removal easy and tool free.