To get started with songs, first things first: get the free ones. They are:
Am I Crazy by Little Fish
Headphones On by Miranda Crosgrove (iCarly tie-in)
Still Alive by GLADoS (Portal tie-in)
Promised Land by Vesuvius (The Rocker tie-in)
Dreaming of Love by Lights Resolve
Charlene (I'm Right Behind You) by Stephen and the Colberts (The Stephen Colbert Show tie-in)
Also, while the normal price is $2, there's plenty of $1 songs from the Rock Band Network, as well as DLC from smaller bands and tie-ins to other movies or TV shows.