Success! After a good deal of practising on scraps and of tension-adjusting, I finally managed to make a nice satin stitch at the bottom of my skirt. What I did was a lettuce edge: since my fabric was cut on the bias, and as I pulled on the fabric while stitching, the hem "curled" up with the satin stitch.
(sorry, Seb wasn't here to take a pic of me in it)
If you click on the pic below, you'll get a closer view of the edge:
(The fabric isn't really that bright, but it's a rainy day and I had to use the flash)
I hope I don't sound too proud of myself... I'm usually not that enthusiast about a finished project - always think there's a flaw somewhere, or that it looks hand-made anyway. But I'm really happy about this one - and this is my first garment made on a sewing machine. I feel I will wear it, and not feel self-conscious. Besides, it's comfy, because there's an elastic at the waist and it's lined.I still need to check if there's leftover fabric to make a matching top... Hopefully there is!