In terms of first songs, it varies on the teacher.
My tsugaru teacher started me on Rokudan Jongara - but only because I had a background in regular min’yo. Bachido’s initial song is Kuroishi Yosare Bushi, which is much more digestible than the denser Jongara arrangements.
A friend of mine usually teaches his students Ecchuu Owara Bushi or Kokiriko first. My regular min’yo group begins with Kokiriko (for dudes) and Ringo Bushi (for ladies).
Dang it! I always get those two mixed up. 
Thanks for the clarification on the two songs. They sound a lot alike at the beginning, but diverge a lot at the end. Interesting history in the two pieces.
Maybe it’s because of the positioning of your left hand? When you have problems with reaching ichi no ito you should rotate your whole hand, so your fingertips and your palm are exactly perpendicular to the strings, you know what I mean?
I’m currently in my 4th month in learning Shamisen. My hand and wrist positioning are still a little awkward.
I bought the fujaku which helped with using the higher tones like 9 and above. As a beginner I found that those were ones I used the least.