Have a look at the Marriott chain. They do a best rate guarantee which matches the price, AND beats it by 25%. We stayed at the Marriott at Washington Metro Centre for about USD$117pn in November last year using this deal.
As for the train, yes, the 2 trains are identical, except the Acaela just stops less. And yes, definately get the red cap. It was madness all those people scrambling for seats in general boarding!
Can +1 for both the train to DC and the Marriott Metro Centre. I took the NE Regional Train which although was slower than the Acaela (only by 30 minutes) was a nice ride and not as full as the Acaela which made seating and luggage easy. I didn't use the Red Cap service and given the light load on the train I was glad I didn't, but a full Acaela may be another issue.
The Marriott Metro was a fantastic hotel. Coming from a tiny NYC hotel room to a roomy DC hotel with a king bed was a nice treat. Starbucks outlet in the lobby, great location and easy walk to the Mall. Enjoy DC, look into the Segway tours for the Mall. I wish I was aware of them when I was there!