Hi Laura,
It's good to see you tackling the pedal steel, though I find it messes with my dobro technique a bit, and vice versa

I guess there is a good reason Jerry Douglas doesn't indulge, though Mike Auldridge did.
My recommendations for tunes to learn would be:
Hickory Wind - The Byrds and/or Gram Parsons
Teach Your Children - I know, I know, lots of steel players turn up their noses at Jerry Garcia's playing, but this is such a milestone in country rock it can't be ignored.
Together Again - there are may different lessons for this classic tune on YouTube.
I hope this helps.
Cheers, Chris