2001 e320 4matic wagon about 120k mi.

My daughter uses it mostly, has had a couple episodes of not starting - cranked but no start, tried a couple of times then started. Usually has check engine light after this which goes away in a day or so...

Checked battery voltage car off no load got 12.5v. I believe this may indicate a battery on the way out? And low battery can cause a variety of similar simptoms?

Otherwise cam position sensor?
I know I should get a code reader, will order one of the ones that cost about 155 launch creamer vII + that should read most codes.

Any advise - should I go ahead and get a new battery?
Thanks
Paul