Hi, @akipponn.

A knitting machine is great fun actually, but I'd tell you about two things : they're a bit noisy :D and also when you knit you only get 'stocking stitch'. I mean one side (that you do not see) is 'knit' and the side that you see when moving the knitting carriage is the 'purl' side. The result is a very smooth fabric that will roll.
You used 'garter' stitch, ie knit on both sides.

If using a knitting machine, you would either need a garter bar which lifts all the stitches off the machine and then you turn the work ... or a more 'expensive' machine that can combine (eg with a ribber).... Perhaps @kimmac has experience with this sort of machines.

I've got (at least) one old Brother machine and you can actually get second hand machines 'easily on ebay' - no problem. I like them because they're 'mechanic' (ie no electricity). I've also got one from Freecycle (do you have this sort of thing in Germany?)
Incidentally, by chance I saw a washcloth (30cmx30cm) knitted in organic cotton for about £10.
Many apologies for my long comment :D I love machines ...