By default character preset includes both morph and material settings. You can also use a Pose preset, again you will need to adjust what is selected. Those are of course DAZ Studio options - if you are using Poser you need to save a pose and edit it, by hand or using one of the availabale tools, to remove the non-morph settings (I think that’s still true), though for faces you can save an Expression and that will work as is.
Yes, I think Save As…Character Preset is what you want to do. You can turn off the material settings, especially if you want to redistribute the character. When you choose Character Preset, it brings up a dialog box that lets you choose what you want to save…you can deselect materials. Other ways to save might work too; I haven’t explored them all so I can’t speak to the pros and cons, but I think Character Preset is the most straightforward. You might experiment with the new DS4.5 DSON format too.