"Good" songs and "popular" songs are often not the same. XD Sorry, but modern music (at least in America) isn't very good.
All the music I have to suggest isn't in English.
Here's a song that's in Japanese, covered by a Nico Nico Douga singer called Valshe. She's quite popular for her boyish type voice, which is why she does so many covers of a shouta-type character called Len.
The song is called Soundless Voice, and it's basically about a boy (Len) missing his twin (Rin) who died. (Lyrics here: link) It's very sad.
Some of the notes are rather low (they're at the very bottom of my range.)
Oh, and if you're interested- there's a sequel to it sung by Rin (and covered by Wotamin) called Proof of Life.
I assure you it's popular among the fans of the type of music I listen to. XD
You could sing anything by Valshe. She has a very low voice so you could probably match her pitch in almost any one of her songs. You could sing Halo by Beyonce, In Your Eyes by Onew, U by Taemin, or Hello by Nu'est.
Battlefeild- Jordan Sparks. For some people might sing this and sound like there voice is really tight and strained during the chorus. So sing this to someone and then have them tell you have they feel you sound.
Anything by Black veil brides, sleeping with sirens, or Linkin park but if you're not into then I suggest anything. I'm an alto and I can do a little of the soprano part. Every alto in my choir can. If you want a hard song then you should try Scarborough fair. Also anything from pitch perfect or pitch perfect 2 would work. Lastly you can take any song and do it in your pitch. It feels weird but you'll get used to it.