TL;DR It shouldn't matter that much what their degree level is. Your affiliation will probably make the most difference, to the extent that it makes a difference.
When I was an undergraduate, I had a job as a research assistant in our chemical engineering department.
We did not have any graduate research assistants at the time in our group, and we published two papers in my time there (had no problems with publication). It was a joint ChE/EE project, so each student was listed by the department that handled their major (if you're admitted into the degree program, you're affiliated with the department). The senior faculty advisors took the final author slot, and they motivated us by offering the position of first-author to the one who contributed the most. There were a dozen of us, and we did quality work. We wound up with a lot of co-authors on one of our papers, but I wouldn't hesitate to say that each made significant intellectual contributions to the work.
I was struck by the comment that you wouldn't publish work done by a student who leaves with a BS thesis. Any student I've worked with would be thrilled to know their research went somewhere, rather than occupying an empty shelf. If you don't think their contribution was significant enough to deserve co-authorship, include them in an acknowledgement, that's what they're for.
As a senior researcher, your job isn't to do the actual experiments. You're there with the big ideas, and the know-how of what probably won't work. Rarely do I see a professor in a lab; their time is too valuable.
I would recommend you reconsider publishing students' managed contributions. Under no circumstances should you take credit for their work, but sending them an email with something like, "I thought you did quality work on this project, and would like to see it published! If you can do x,y,z, we can submit it to a journal together. If you aren't interested in publishing it with me, I could include you in an acknowledgement, and it could still make an impact." would usually be met with a positive response. The whole process would be very helpful to any student considering graduate school.
Facts are not copyrightable, and university student conferences don't serve the same purpose as peer-reviewed journals. If you're concerned with copyrights on the figures, you should make better figures for the paper using the same (non-copyrightable) data [though you can hold a copyright on a collection of data]. Chances are the you'll want different figures by the time the paper is finished anyway.
Maybe it's colored by my experience, but to me final authorship is a stamp of approval from an experienced researcher who is personally vouching for the work with their reputation. The final author should obviously be very involved in the research process, but doesn't necessarily need to have done all of the work by themselves.
I've heard of people who have problems publishing because they didn't have a university affiliation, but the affiliation of any individual will probably suffice for the whole, to the extent that matters. You still have to get past peer-review, and should still make sure the writing is quality. Undergraduates may especially struggle with quality literature review, but I strongly recommend involving them in the process. It's what pushed me towards a PhD.