Finally, I did it. And it was so easy too.
Yesterday, I sorted all my beads with 5mm holes into those that fit the Sterling tube I've got and those that doesn't.
I changed the peg on my untill now unused Impress Beadliner and tried for the very first time my tiny tubecutter, my de-buring tool and my somewhat unprecise calliper.
I read the instructions and proceeded to line my first bead. It was easy! I don't know why I have to wait so long to try a new thing, I do that most of the times I try new things by myself when it really isn't all that difficult. I am working on that :)
Anyway - here are my 3 first cored beads. Now all I need is a Dremel/-like tool to polish up the inside of the tube, that hid a white surface I hadn't noticed before. And some more tube of course :)