Would it help if I told you that I started sewing knit fabrics about two months ago and have had no problems treating them pretty much the same as woven? Nobody told me I was going to have problems, and I haven't had any.
I have no overlocker or coverstitch machine, I have just used straight stitch and zigzag, although I did use a twin needle.
Common sense says that you shouldn't stretch the fabric while you're stitching it (although it also says it's much easier to absorb a little slack on stretch than on woven
).
I've even sewn woven to knit for the StyleArc Annika. Easy peasy.
I have to admit that I haven't sewn anything super-stretchy, just normal stretchy, but I don't like super-stretchy clothes anyway.