Great ideas and input! I went and got one of those Rubbermaid storage bins to set the Tutto in. I wasn't really sure if computerized machines were meant to be laying on the side either. I always thought it'd be best to keep them upright. I saw a blog where someone was reviewing her Tutto with her computerized sewing machine in there and it was laying on its side in the trunk, which made me start to second guess myself.
If it turns out classes are a regular thing for me, I may just consider looking for a class sized machine. Something more lighter and compact.