If you haven't taken any kind of formal lessons of your own, Hal Leonard series instructional videos and books are fantastic. They're a standard in many school districts and are very straightforward.

http://www.halleonard.com/

You might try getting a beginning piano teacher too.

IMO every musician regardless of what instrument is their main one should learn some piano.

AND...more and more each year I feel that every musician should have a teacher at some point.

The more I play with self-taught musicians the stronger I feel about it.

Don't get me wrong...I've taught myself how to play a lot of things...the best musicians learn the most through experimentation on their own.

I just think you really need a teacher at some point to become a complete player and like I said I'm seeing proof of it everyday.

Piano was my major.  I took up drums at 45...2+ years ago and I can't imagine how far along I'd be without my piano background, given my age.
Independence has not been a problem, reading multiple notes at a time is easy and so is hearing what is going on in the music.
In the beginning the main difficulty was overcoming the programming that notes high on the staff were for the right hand and were placed to the right of the body (etc).  I felt like a dyslexic for a while, but once I realized why my body was going in the wrong direction so many times it was easy to fix.
I think that having some melodic and harmonic understanding also plays into how I appoach playing the drums.  If anything has been a drawback for me, it has been the dependence on notation reading that classical training gave me.  Improvisation has been my weakness, kind of scary even!  But I'm starting to enjoy it ...especially as my skills build.
Drumming has even improved my piano.
I agree it's a good combination!