I wouldn't be surprised if LaRoche's option is agreed on for next year, but I think he'll be our legit every day 1st baseman for a long time.
I think Michael Morse will be the first guy to succeed LaRoche at 1B, whether or not LaRoche remains with the Nats past this season. I think Morse will get an extension on his current contract and up playing for the Nats through at least 2014/5. He is still peaking as a player and he is in good enough shape he can hold down 1st or LF for a while. Eventually I think you see 1st base turned into a pseudo-DH spot for the Nationals. I think by 2015 you'll see Werth and Zimmerman getting occasional days there and even Bryce if he grows much more. If not Michael Morse, maybe you see a guy like Tyler Moore or another bopper get put there to hold down the spot most days while other players moonlight there for easier days.
I think it'll be a long time before you see the Nationals go out and try to find a first baseman like Prince. A big time slugger would be nice, but keeping 1st open give you a lot of option and huge flexibility.