Starter problems

As you have mentioned it yourself, it could any of those items.
 
Obvious place to start is to test out the battery voltage with a meter.  Assuming you might not have one, when you turn your key, do the dash lights go dim or does the intensity remain the same?

Is the problem intermittent?  What vehicle do you have?

You could eliminate the starter switch by, by-passing the switch.  Take some bridging wire, long enough to reach between the battery and solenoid.  There is another point at which you could take power from to bridge the solenoid, which means a shorter wire, but you have not given details of your vehicle.

With the vehicle in PARK, HAND BRAKE applied, hold one end of the bridging wire firmly to the solenoid connection (not the wire from solenoid to starter, the other point to which a wire from the loom goes to the solenoid) and get an assistant to make contact with the other end of the bridging wire, with the positive terminal of the battery.  NOTE, when contact is made with the battery, there will be some arching, so the connection needs to be be made quickly and held firmly, don,t chicken out, otherwise you will have more arching than necessary. ends, check to see if there any signs of melting, arching, loose connections; that being OK, suspect the switch. 

When contact is made, there starter will throw and and turn. The starter working ensures the solenoid and starter are working, other wise you need to your attention to starter and solenoid.  An auto electrician can re-condition the starter at a fraction of the cost of a re-conditioned or new starter.

With the starter working, then turn your attention firstly to the socket connection to the ignition switch.

Check to see the condition of the terminals of both