European new to the Major League Baseball

Like I have mentioned in other posts, the MLB have never really fully interested me, but I have also never stopped thinking about looking for a team to root for and follow the league more for real.

So if I were to begin following the league more now, which team would be good for me as a european to start following? Could you help me a bit to get going with this?

Some things that can help
- Don't have to be the best team, a underdog interest me more than the team with the best team who wins all the time.
- Canucks, Vikings and Arsenal fan
- I am from Sweden
- Good logo is always nice

Are rivalries a big thing in MLB? If so, a team with a good rivalry would be nice.
From what I know, some teams I don't want to root for are Astros (the cheating thing), Dodgers and Yankees (seems to get the best players and win all the time), Red Sox (as a Canucks fan I don't like Bruins and in the NFL I partially because of that don't like Patriots) and then maybe Brewers because of MIN vs MIL (Vikings v Packers)

Could you also maybe give me some things and rules I need to know about to really enjoy watching the games and understand the things happening?