If you are going to throw parts at the problem, the battery is FAR cheaper than a starter.

If you are from the "old school" of car ownership, an anemic battery could still turn the starter (albeit, very slowly). This would make an easy case for the battery.

Cars since the mid-80's are a lot smarter. The engine management systems measure the output from the battery, and if it is insufficient to crank the starter, it will shunt the circuit to the starter solenoid, so you won't get anything but a "click"!

I have witnessed this in every car I've owned since '86, and 100% of the time, the battery was the culprit!

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car