Its still possible to have a good singing voice even if you are not born with the "tubes" but it requires more work.
If your not natural you have to train yourself to LISTEN! Most people have no idea what is coming out of their mouths 'cause they don't listen to what they're sounding like............if you hear a certain tone, can you duplicate it with your voice?
The most simple way to do this is to REALLY LISTEN, in a way that most people who aren't musicians never do,to music. Most people "listen" to music as a background for their life and conversations with their friends.........not to really listen to the music. Try and break your favorite song into each of it's constituent instruments........listen to JUST the drums and then FOCUS on just the base.............same thing with the vocals......especially if there are harmonies.........but mostly just learn the song.........know the song so well that........to sing it to yourself again would be almost painful.........the only purpose left is to sing it for someone else......to share it........and then you get back all the energy you put into learning the song!!!!
WRITING DOWN THE WORDS HELPS TOO. But learn the song so you don't need the written stuff.........
Hope this helps
Doug

doug again..........didn't see the end of your question.........just go for songs you love..........if you have to work hard.........could you do it with songs you don't like??? Nothing else matters...........you can sing...learn the song and SING!!