You could drive to stamford and park there. Then you would have the option of either express and local metro north trains to grand central. Make sure you pick the express. It seems clear you don’t want to park in new haven. Other options are milford, west haven and bridgeport.

If you are dead set on getting on the sub way - i’ve done it before in both queens and the bronx. Just pick an express subway stop and see of there are parking garages. In queens - i used to live in forest hills and i know the e and f lines are express at the 71 ave stop. There is a parking garage not to far from that subway stop. In the bronx - years ago i googled a stop on the subway that was express not to far north of i-95. Then i made sure there was a 24 hour parking garage in advance. It worked out - but i forgot where it was.

Yes you can buy tickets on the train from the conductor but its more expenisve. You can buy tickets at the kiosk machines in the stations or beside the tracks or at the ticket window.

If there is traffic on the road - the train save time. No traffic - the car is quicker.