My favorite, with their all-time classic:
Also can't go wrong with Bad Religion, Less Than Jake, Goldfinger, The Ramones, and pre-Sing the Sorrow AFI.
Also, if you listen to The Offspring, pick up their self-titled album first. It's far and away their absolute best.
These are the bands I listened to in my teenage years; I don't have much experience, and I admit I was introduced to my favorite punk bands almost entirely by the first 5 Tony Hawk games. Haven't been into punk since 2004, but I still love the ones I listed.