by Robert Brenstein.
As far as I know, upgrading 1.9.3 to 1.9.19 first is not an option but a requirement for successful upgrade to 2.2. I would also second Colin's suggestion to first get 1.9 working on the new server before going further to 2.2. As you say yourself, it is a big jump. While most people made the transition without much ado, some ran into issues as you can see searching this forum.