I'm in the very beginning and followed Hadar into the barracks, by chosing him did I make a desision that affects the rest of the game or just the opening?

Don't worry ... it's just the opening ... you can go whichever way you want after the prelude ...

Not really, but it does dictate whose house you get to loot in Riverwood. I prefer being able to loot the smith myself.

Other than that, nothing really, but you do get to hear both sides of the civil war by talking to your rescuer's family in Riverwood.

No, that's the beauty of Skyrim. You can choose who to join when you are good and ready! Now, talk to the smith in Riverwood, make some new armor, go clear out the bandits in the mine, to get some experience, oh and stop by the Guardian Stones and choose your first sign (before you get to Embershard Mine and Riverwood).

Have fun, new Dovahkiin!