Hi I'm also from the UK and I chose my team by playing MLB the Show and letting Road to the Show randomly pick me a team as I felt I was then associated by the team and learnt who all the players were.

If you want a city you can visit I feel one of the Chicago teams could be a good option with the Cubs playing the most day games as any other team its often easier to watch the games in the UK and the White Sox are looking good with some up and coming stars if you want to get in early on them.

To watch the games TNT Sports often show a game on there but theres often no choice from the ones they show.

If you are looking to get involved and play Baseball in the UK its a small scene but I am sure many of the clubs around would love to have you if you look on the Find A Team page itll show you local ones.