Check the starter relay connections and tighten or remove/clean/replace them and try it. Make sure you grease those bad boys so they don't corrode.
I'd start with a few tests before replacing the starter.
Using a jumper wire, short the trigger wire terminal on the starter solenoid directly to the positive on the battery, remove the trigger wire to do this. Make sure it is not in gear. This will turn over the engine regardless of any thing else in the system. The key doesn't need to be on and the starter will turn as soon as you hit the battery terminal.
If the the starter still clicks, clean ALL the battery cables and try again. This includes the Positive at the starter and the Negative (ground) at the ground point. Also check ground strap from engine to frame.
If it still clicks, disconnect the battery. On the back of the solenoid is a cover with 3 screws. Remove the screws and cover carefully noting the spring placement and direction. Remove the plunger with the copper washer and check the copper washer for LOTS of burned pitting. If it is bad, turn the copper washer over and reassemble. Connect battery last and test.
If it still clicks, remove the starter and bench test. In the service manual there are specific tests that can be done to determine the failure or replace starter. If you don't have a service manual, I suggest you get one because it can save you some time and money. And it has all the correct methods, procedures, and torque settings.
Hope this helps.