My biased opinion: Boston Red Sox
Smart, successful ownership, one of the best GMs in baseball and a great manager (both good guys too), tremendous fan support, oldest baseball stadium in MLB, lots of money, two World Series wins in the last 5 years -- combine all this and you have a team to root for that is pretty much guaranteed to be very good nearly every year. Plus -- think about this -- being in the UK, it would be hard for you to read a lot about most other teams on the internet, but that's not the case with Boston. You probably can go to 5-6 local papers online everyday, and a bunch of blogs and forums devoted solely to the Sox. Hours and hours of new material every day to read if you want to. And you will automatically become engrossed in the biggest baseball rivalry on the planet, versus the New York Yankees. That rivalry exists 365 days of the year as they try to steal the biggest free agents and amateurs from each other, and try to out-perform each other with trades. (and 80% of all other fans are annoyed by your team
)
My unbiased opinion: (Red Sox excluded) Minnesota Twins -pretty good record most years, excellent management, getting a new park next year, one of the best mid-size teams.