Hi, and welcome to the forum.
You're on the right track. The first thing I would check is the battery. Have it load tested at an auto parts store.
If the battery tests O.K. next check the solenoid, jump across the main terminals with an old screw driver. If the starter turns over its the solenoid.
If the solenoid is not the problem check the battery cables, if you twist them and they kinda crunch you probably have corrosion and they need to be replaced. Also check terminals for corrosion, clean and coat with dielectric grease.
Lou