I started out 10 years ago, just like you plan to start now. Part time, doing stumps for a friend who owns a tree service, but who does not want to fool with stumps.
Don't waste your money on one of those little "backbreaker", underpowered handlebar machines. Look for a good used Rayco 1625Super Jr., or similar size machine. A machine with at least a 25hp air-cooled engine is the minimum size you should consider. This size machine will handle about any job, but can be slow on big stumps. However, they are a heck of a good starter machine.
I started with a Super Jr. and made a heck of a lot of money with it. Easy to operate, and simple to maintain and repair.
Jeff