Based on what you did the solenoid on the side of the starter is bad. Nothing when you use the key means the windings in the solenoid aren't pulling it in when you supply power to them. The way it works when it pulls in it both engages the bendix into the flywheel ring, and closes a set of contacts to energize the starter. The fact you were able to jump the posts means the starter itself is more than likely OK, but without the solenoid energized the bendix will not kick out to engage the flywheel ring.
In other words, Yes, you did the right thing pulling the starter. If it were mine I'd take it to my local repair shop and have them go through the whole starter, even though just the solenoid appears to be the problem, just to be on the safe side. More than once I've taken one in with 'just the solenoid bad' to find bad brushes, a dry bearing, etc, etc in the main body. Basically it's well worth the little extra cost to get it all checked to insure you won't be pulling it off again any time soon.