Can you tell me which clubs should I watch ?
For the NFL, I would recommend teams like the New York Giants, Dallas Cowboys, Green Bay Packers, New England Patriots, Pittsburgh Steelers, and the Baltimore Ravens.
I am not too sure about the NHL, I have limited knowledge on that so you might want to ask someone else about that, but I guess the Rangers would be a good choice. Boston Bruins, Vancouver Canucks, Washington Capitals, and Chicago Blackhawks are also good teams to follow.
Any specific rivalries or something to pay attention to ?
Not sure about the NHL, but for the NFL these are great rivalries
New York Giants vs. Dallas Cowboys
Green Bay Packers vs. Chicago Bears
Pittsburgh Steelers vs. Baltimore Ravens
These are divisional rivals, they have more meaning in the NFL than they do in the NBA.
But FYI, I just gave you a bunch of contenders. I wouldn't want you to cheer for some terrible team like the Colts without Peyton Manning or the Jacksonville Jaguars.