@aprilla I have used both the overlocker and coverstitch to sew light and medium weight sweater knit fabrics, bought and made on a (standard guage) knitting machine. I've also sewn a couple of hand knits. On the coverstitch the single needle chain stitch can be very useful for seaming hand knits with finished edges.
On both the overlocker and coverstitch I prefer to use woolly nylon / polybulk thread in the loopers.
On the knitting machine I tend to use the finer yarns and they can work well in the looper instead of the woolly nylons as long as it's smooth and not a boucle style (same goes for the overlocker loopers).
The fine and lightweight knits can be overlocked and coverstitched just as you would stretchy lycra style knit fabrics.
Fine looser knits you treat as you would any mesh type fabric.
This cardigan is one I made from a fine lightweight sweater knit fabric bought from Fabworks
This boat neck pullover is a looser sweater knit that is more like a mesh, bought the fabric from Minerva
For thicker, spongier and looser knits then use things to help you like tearaway stabiliser, water soluble stabiliser (WSS), Gloop (made from WSS scraps), tapes and elastics.
Play and practise with the settings including foot pressure settings and the differential feed and stitch length settings. Use up your swatches and if you don't have any, pick up some old or ugly pieces from a charity shop and use those.