I started my music listening journey last year when I first fell in love with The Offspring when I encountered them in.. yes.. Crazy Taxi. Here's some punk recommendations:
The Offspring: Self-Esteem, All I Want, Mota The Future Is Now, The Noose, No Brakes, Change The World, Way Down The Line
Rise Against: Prayer Of The Refugee, Savior, Re-Education (Through Labor), The Numbers, Broken Dreams Inc.
Bad Religion: Them And Us, Punk Rock Song, Nothing To Dismay, Epiphany, Emancipation Of The Mind
Other punk bands I'd recommend: Sum 41, Rage Against The Machine, Billy Talent, Millencolin, Goldfinger
Later in May of this year, I started veering into heavier stuff, more alt-metal but not quite fully committing to it. Through this period, I encountered many great bands including:
System of a Down: Chop Suey!, ATWA, This Cocaine Makes Me Feel Like I'm On This Song, Attack
Seether: Fake It, Remedy
Disturbed: Down With The Sickness, Indestructible
Finally, entering into my current period of music listening. Since July, I've been almost exclusively hooked to grunge/alt-rock from the 90s and 00s. Such examples include:
Audioslave: I'd say listen to everything but you wanted recommendations so: Be Yourself, Wide Awake, Drown Me Slowly, Show Me How To Live, Out Of Exile, Sound Of A Gun
Soundgarden: Black Hole Sun, The Day I Tried To Live, Burden In My Hand, Fell On Black Days
Alice In Chains: Heaven Beside You, Your Decision, Down In A Hole
To wrap up, LISTEN TO EVERYTHING ON THIS LIST! Beautiful fucking songs.