Starting car

This doesn't exactly sound like an alternator to me. Sometimes it starts and sometimes it doesn't? If it was the alternator, it would start once, but your would slowly lose power to your accessories/lights and eventually stall out. Then, without jumpercables, or a new battery, it won't start again.

Do you have power to your accessories/lights? If you do, then the alternator's working fine.

Could be plugs/wires not sparking properly all the time to turn the motor over - could be mis-firing cylinder - Could be a weak starter.

I'd take it to a couple shops to see if they agree on what it is before getting it worked on though.

I had this happen and it turned out to be worn down copper connectors in the starter solenoid,
I built them back up with silver solder and it worked fine as long as I owned the car (several years).
Most people would probably replace instead of attempt to repair the solenoid (I was stuck in the middle of nowhere).