I usually drive from Hartford to New Haven and take the train to Grand Central, however when I am feeling exceedingly lazy there's always the bus from Hartford to Port Authority. Parking at the New Haven train station is only a problem during the week- I've never found the garage/lot full during the weekend. And even during the week, there are other lots in the area and there is a garage about 15 minutes walk away that has a shuttle to the train station.
Regarding furniture, it really depends what you're looking for. I was impressed by Fly By Night up in Northampton, MA for high quality apartment furniture. And I'm sure you know that we finally got an IKEA.