Joe V,
I think you've gotten some really good advice from the forum folks. Here's my two cents for what it worth.
I picked up the guitar when I was about 13 and learned from a group of friends. We all learned by doing and playing songs we liked. I could only afford one acoustic guitar so I focused on strumming and fingerpicking. So it was all about rhythm and chords.
After playing guitar for 3-4 years, I started tinkering with piano. My high school music teachers helped my learn basic music theory which I applied to the my piano playing. I learned more in those first couple of years than I did 20 year hence. Again, I focused on accompaniment and hardly ever played the melody since I had that covered by singing. I could read music a bit but was mainly just following the guitar chords in sheet music, tabs and lead sheets.
Well, about 25 years of real life and military career that kept me moving every couple of years, I finally put down some roots. I had hit the wall with my piano skills and wanted to do more so I started taking some lessons. Wow, a whole new world opened up. I discovered I actually hand a left hand and ten fingers. I guess all I'm trying to say is that sometimes you need help getting to the next level, be it a group of friends, a well place high school music teacher or a dedicated piano teacher. Self-learning can be a rough way to go and you can pick up a lot of bad habits that keep from getting better.
Good luck and have fun!
SD