well, you can find rear sprockets on e-bay pretty cheap. Yes, all coaster brake hub sprockets are the same and they are held to the hub with a snap ring. If you are unfamiliar with taking a bicycle hub apart, you best bet is to take it to a bike shop and let them do it.
Chaning a rear sprocket is about a 15 minute job start to finish.
going to a smaller front sprocket woudl give you the same results (like going from a 44 tooth to a 36 tooth) but changing the frint sprocket is a little more work.
Another thing to consider is that you may have to lengthen or shorten your chain depending on how much chain is on the bike, and which sprocket you change.
any time you want easier peddling (lower gear ratio) go to a bigger rear sprocket or a smaller front sprocket.
for the engine rear sprocket, if you want more torque for hill climbing, you woudl go with a bigger sprocket.
a bigger rear sprocket in this case, lowers the gear ratio and a smaller one will rais the gear ratio.
for the engine gearing (because the engine sprocket is a 10 tooth), a bigger rear sprocket will give you more torque on take off, faster acceleration, and better hill climbing ability. but there's a trade off, your engine will rev slightly higher at cruising speeds, and your top speed will go down.
If you want more top speed and less take off torque, you would have to go with a smaller sprocket.
a smaller sprocket raises the gear ratio, and give you more top end speed.
this is not good for climbing hills because you lose low end torque and acceleration.
the cruising rpm's will be lower with a smaller rear sprocket and the fuel mileage will go up slightly. but your top end speed will increase quite a bit.
