Oh my, my friend. This list is going to get long. I'll give songs instead of artists, because it's just better that way. If you can't find the song, don't hesitate to PM me and I'll post the song on sendspace or something. These are just beginner songs to the bands I crazy enjoy, or albums that I think are essential. (things are separated by semi-colons for bands, and songs are separated by commas).
"It's There" by All Girl Summer Fun Band; "Aaron and Maria" by The American Analog Set; "It Was There That I Saw You" by ...And You Will Know Us By The Trail of Dead; "Fair" by Annuals; "Judy and The Dream of Horses", "Get Me Away From Here, I'm Dying", "The Boy Done Wrong Again", and "I'm Waking Up To Us" by Belle & Sebastian; "Don't Forget to Breathe" by Beulah; (only download these songs if you're into screaming spastically, and loudness) "Burn, Piano Island, Burn" "Every Breath is a Bomb", and "Love Rhymes with Hideous Car Wreck" by The Blood Brothers; "Jetsabel Removes the Undesirables", "You Will. You? Will. You? Will. You? Will", "Sunrise, Sunset", and "It's Cool, We Can Still Be Friends" by Bright Eyes; "Lloyd, I'm Ready To Be Heartbroken", "Happy New Year", and "Books Written for Girls" by Camera Obscura; "Lonesome New Mexican Nights" by Casiotone for the Painfully Alone; "The Great Decay", "Fairytales Tell Tales", "The Game Of Who Needs Who The Most", "The Lament of Pretty Baby", and the whole Ugly Organ album by Cursive; "Here I Dreamt I Was An Architect", "July, July!". "The Legionnaire's Lament", "California One" by The Decemberists; (for annoyance and fun) "Panda, Panda, Panda" by Deerhoof; "G*ddamn Lonely Love" by Drive-By Truckers; "I Want To Hear You Sad" and "Sunday Drive" by The Early November; "Everything Reminds Me of Her", "Somebody I Use To Know", "Miss Misery", "Between the Bars", and "Thirteen" by Elliott Smith; "Black Acres" by Elysian Fields; "Other Girls", "Ecoutez Bien", and "When I'm Up" by Eux Autres; "I'll Catch You" by The Get Up Kids; "Hope for Us" by The Jealous Sound; every Just Surrender song; "The Quiet Screaming (Dashboard Confessional vs. Brand New" by The Legion of Doom; "Can I Call You Mine?" and "Pilgrim" by The Long Goodbye; EVERY Lydia song (for serious); "Poison Cup" by M. Ward; "J'ai Deux Amours" "La Vie En Rose" by Madeleine Peyroux; "Giving It Away (acoustic)" and "The Ocean" by Mae; EVERY Margot & The Nuclear So and So's; EVERY Mayday Parade song; "IOU", "Hustle Rose", and "Combat Baby" by Metric; "Cold, Cold Water", "Recommendation", and "The Garden" by Mirah; "Have To Explode", "This Year", "Love, Love, Love", and "Cotton" by The Mountain Goats; "Panic" by Name Taken; The whole In The Aeroplane Over The Sea album by Neutral Milk Hotel; "The Get Go" by New Young Pony Club; "Rapture", "Indian Summer", and "Bad Diary Days" by Pedro the Lion; "Blind" and the whole Without You I'm Nothing album by Placebo; the whole Good Health album by Pretty Girls Make Graves; EVERY Q and not U song; (um, for hilarity) "Let's All Go To The Mall" by Robin Sparkles (How I Met Your Mother joke song); "I Love You Like The Way That I Use to Do" by Rocketship; "Damn, Sam (I Love A Woman That Rains)" by Ryan Adams; EVERY Saves the Day song; EVERY Silverstein song; EVERY The Smiths song; the whole Becoming X album by Sneaker Pimps; the whole When I Explode album by So Many Dynamos; "Indie Rocker" by Sparky's Flaw; the whole Sunsets and Car Crashes album by The Spill Canvas; the whole Set Yourself on Fire album by Stars; EVERY Weezer song; "Hell is Chrome", "Kamera", "Jesus, Etc.", and "Say You Miss Me" by Wilco; EVERY Yeah Yeah Yeahs song