Piano songs or pieces to learn for a beginner?

Hey

I just started learning piano a few days ago and well I love it, but
I'm having a tough time finding good songs to learn for a beginner

So far I have learned Silent Night (First song I have learned)
Ode to joy (Well single notes at least)

I've been working on Fur Elise, but I have been having a problem doing
the runs on them like from the low E to E to G Sharp run and that
frustrating C D B C run that follows the A E A run. My biggest problem
seems to be getting my fingers to stretch and getting them in position
in time. I'll keep trying though, but I was hoping that learning a few
more songs on the piano will help me with this.

Also I have been having a little trouble learning the Halloween theme
and Something I can Never Have (NIN) since I can't seem to get my
right hand to do a pattern in rhythm while I try doing something with
my left hand.

Plus any song or piece suggestions to help prepare me to learn
Beethoven's Moonlight Sonata would also be wonderful because my main
goal is to learn that piece. It's what got me to learn piano in the
first place.

Also if this helps I'm 17 and I have learned other instruments as well
like the drums (kinda odd since I can't keep one hand to do a pattern
on the piano), Guitar, Bass, and I have some history with the
Xylophone.

Thanks to all suggestions. They are very much appreciated.