I do this NY to Baltimore. Like you, one round trip a week and like you, price is important to me.

I buy all my trips for the upcoming period every couple of months. Too far into the future and Saver fares aren't always available during peak times. Too close and they're all sold out. So, you have to time it just right. Right now I'd be buying May-June, for instance. But if you are going during non-busy times, Saver fares will be available now and you can book any ride you know you're taking.

If you are forced to buy Flexible (one bucket up from Saver), it helps to use a student or AAA discount to get 10% off.

Definitely join Amtrak Guest Rewards and think about getting the credit card. I put every single thing possible on it and it nets me 1 or even 1.5 rides free a month.

Every once in a blue moon I will buy a 10-trip, primarily if I'm not sure when I'm going, but buying Saver can beat it by 40%. And I never ride Acela.