It's important that songs are sung, but some are sung more than enough. If lots of people, or even just one or two famous performers, sing a particular song, they're probably doing a good enough job of it, and I can't see much point in anyone else learning and singing it. That's not to say you mustn't do so, but it's not the best use of your efforts, unless you are going to bring something new to it.

Have a go at some songs that aren't been sung so much (or at all), which you can find in such places as The Full English and Kist o Riches, and on CDs available from such places as Veteran Mail Order and Musical Traditions.

And don't bother at all about whether a song you've heard suits your vocal range. There's no law that says you have to sing it in the same key you've heard someone else sing.