Nothing will be completely invisible, but that's okay. As long as you're consistent is what matters most. Garter stitch does show a little more maybe because you are adding extra rows when you do short rows and since garter is ridges those ridges will show up.
I've done garter stitch w/t and and I don't pick up the wraps. If you look very closely you might be able to see the it, but for the most part the wraps just blend with the purl bumps you see. Here's a page to look at maybe it will help.
Scroll down for the garter info -