We do some embroidery at my shop, so here’s my 2 cents
Backings are a must… especially with loosely woven or stretch fabrics. If using a hoop, need to make sure the backing and fabric are taught. Even if you use a backing you don’t want the fabric bouncing up and down - it will affect the stitch. I do a fair amount of “tackle twill” or applique using the zig zag machine on stretch lycra - which can be a nightmare. What works really well is this backing that has a slight tack to it - about as sticky as masking tape - and it stabilizes the fabric really well. It tears off really easy.
Something obvious, but often overlooked… Make sure you’re using the correct needle, that it’s installed correctly, and that it doesn’t have any burrs on it. This applies to any sewing machine. If it ain’t stitching right the first thing we do is change the needle. Also depending on the fabric the size of the needle can affect the stitch - which can be more important with embroidery as you literally can be stitching over stitches.
Also what’s really important with embroidery is your thread tensions. Another tip is to use a thread net on your thread cones… they keep the threads from twisting and / or knotting up - especially with metallics which are prone to twisting. Thread lubricant can also help as it helps to reduce heat build up from friction from certain fabrics or high speed operation.