I think too, playing on a church organ is the best you can do to learn organ playing.
At least so I do it. Don't expect to become a master after only some hours of organ playing, even if your background is long-year piano playing under your belt (so it was in my case as I started additional organ playing).
One thing is, that the pedal part should not be underestimated. First, there is a good relaxed feet position to learn, along with alternating heel-toe playing or for baroque stuff maybe toes alone. The other important thing is, that instead dynamics (what you don't have for a fixed registration) one needs to learn a good articulation - all steps between legato and staccato, differenciated for the different voices one plays.
Often, piano players tend to play all the time legato on the organ, because they think that the lack of sustain pedal must be compensated by legato playing. That's no good idea - things get blurred in the normally heavy reberved acoustic in a church.
You asked for appropriate piano pieces to begin? I suggest Bach pieces, e.g. from WTC or Inventions.
If you look for an easier but good sounding organ piece with pedal part, I suggest the "8 little preludes and fugues" from Bach (it is doubtful that Bach was the composer, but you find the score here). The C major prelude and fugue (BWV553) sounds great, because of the arpeggios, and difficultier as it is, also the little fugue is something special. It was the first piece I played on organ, you can listen to if you like, on my homepage:
The last piece I recorded was the Buxtehude piece with a larger pedal solo at the beginning, so maybe one can see a little progress after one year of organ playing...
Hope it helps a bit.