I sent out a letter and two cards to Orioles 1B Mark Reynolds on July 31 and received the two cards I sent signed on August 8 (and I learned that chrome cards do not take some pens well). Mark's one of my favorite players (MLB record holder for most strikeouts in a season, but also three 30+ home run seasons), and happy with the cards and seeing he's a quick signer, I sent him a baseball on September 7th and received it signed a week later. If this O's team keeps up, I think they have a shot at winning it all, and it's cool knowing one of their key players signs quickly - he's definitely worth a try, especially if the team's at home.
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I used this address:
c/o Baltimore Orioles
Oriole Park at Camden Yards
333 West Camden Street
Baltimore, MD 21201