#1
If you're having problems, start out with easy stuff that you are already familiar with. I learned using EZ Guitar Method or something. I had to suffer through some pretty corny stuff like "Skip To My Lou" & "On Top Of Old Smokey" but it did give me the groundwork for coordinating my singing with my playing.
#2
I started with simple songs where the vocal melody followed the chords being played underneath and didn't have any unnatural strum patterns to it (some may feel more intuitive to you than others). Over time as you grow more comfortable with it things become easier. At first I didn't think I'd be able to do sing and play at all but eventually it will "click".

It definitely helps to have the lyrics memorized or on a sheet you can read off of as well. It takes a lot more focus because you have to be very conscious of what you're playing underneath it, as well as when vocal lines start and end.

That's about all the advice I can give to anyone trying to learn to sing and play.
#3
I think the early stuff from Black Sabbath is ultimately the best way to learn singing and playing simultaneously. Simply because the vocal melody follows quite exactly the guitar riff, just like in Iron Man or Paranoid.