Starters rarely "stick" or jam.
There are a number of things which could have happened.
Battery cable problem.
Connection problem.
Fuse problem.
Solenoid problem.
Starter failure
If it were me, I'd get the factory service manual and use engine electrical and engine controls diagnostic information to troubleshoot the problem. You may find that is more economical than just starting to replace parts.
On the other hand, if trial and error is the way you're going to go, understand that you're simply ignoring a host of potential electronic problems which could cause a no-start condition but have nothing do directly with the battery, cables or starter.
That said, I'd inspect all battery cables and connections from the battery down to the starter and from the battery to ground. I'd inspect all the engine controls grounds. If things look good there but you still only get a "click" from the starter, you can try replacing the starter.