It depends on time of day if you can do it in an hour or not, but since you say peak fares have not kicked in it's either early morning or early afternoon, so an hour is doable. The difference between peak and off peak is not a ton of money (under $5) so it's not worth going nuts over. Depending on the train you get on, if you board at 125th there could very little chance of a seat, so you may stand for an hour or so till seats open up after the first few stops.


For the return either train works. Amtrak is more expensive, but the seats are more comfortable. Out of New Haven you will pretty much always get a seat on Metro North (since the train is probably starting there) unless you are on a peak train and show up thirty seconds before they close the door.

I would save the money and take Metro North / Subway / Airtrain instead of Amtrak.