The above solutions are very good, but I think it's also worth noting that DLC counts towards the 20 songs, so if you have/wouldn't mind buying some of it, you can make this achievement a little easier. The free songs are a little challenging, but if you are having trouble, why not try them out? Here are some easy DLC songs:
Halo Theme MJOLNIR Mix
Top Gun Anthem
Messages (Velvet Revolver Pack)
Super Massive Black Hole (Muse Pack)
God Put A Smile Upon Your Face (Coldplay Pack)
I Predict a Riot (Isle of Wight Pack)
Tina (this comes with the GH3 soundtrack, and can also be downloaded on XBL)
As for what other songs to go for, that's personal preference. Depending on what you're good at doing (keeping rhythm or hitting hard solos, etc.), you may find some songs more difficult than others. The other solutions here give good suggestions, but here are my personal picks:
Songs To Start With: Story of My Life, Mississippi Queen, Bulls on Parade, When You Were Young, Lay Down, My Name is Jonas, Sabotage, Reptilia, Closer, Generation Rock, Metal Heavy Lady, Radio Song, Ruby
More Difficult Ones: Slow Ride, Talk Dirty To Me, School's Out, Sunshine of Your Love, Miss Murder, Paranoid, Anarchy in the U.K., Even Flow, Can't Be Saved, She Bangs The Drums
Now, the other solutions here mention some songs that I'd personally stay away from- Avalancha is one. This song has a fairly difficult part at the very tail-end of it; I found it quite annoying to FC and gave up. The other one is Cities On Flame. I think there are 20 songs waay easier than this.
There is one more trick I can give you here. Since you don't need to FC (keep a streak for the entire song) 20 songs, but just get 100%, you can wildly strum through fast parts that you are shaky on just to make sure you hit every note. There are two songs this helps with: The Seeker, and Black Magic Woman.