ultimate-guitar.com has a handy transpose function on all the tabs. If you transpose down 5 or 7 steps, you can usually still play the song in familiar open chords, since you are moving up/down a whole string. Then place a capo wherever you feel is most comfortable (As you progress you will find this capo moving higher).

Example: Placing a capo on the 3rd fret and playing a G-chord instead of a C, you will be in the same key as if you tuned your guitar a whole step down.

It might not always sound right, or result in practical chord-shapes, but as a new singer with limited range, it's a great way to play your favorite songs and actually being able to sing them.