In the past I've used Fabrico ink pads and acrylic paint with fabric medium.
I like both ways.
I think the paint holds up better in the wash. It's stiff at first but softens after washing.
I find that more of a pain to mix (I use those little white paint pallets) all the colors BUT you have more color choices.
I'm pretty sure the fabric medium instructions said just a few drops can be added to paint.
When I mixed it I had paint about the size of a dime/nickle and added 4-5 drops of fabric medium.
Never had any trouble.
The fabrico inks hold up well to washing but not GREAT. I was happy with them - maybe my expectations are low.
FYI - I like the 1" Fabrico pads so I can get into smaller areas. I bought mine here:
http://polymerclayexpress.com/inks.html
They have the re-inkers, too.
I've never tried Sharpies or StazOn - can't help there.
I've stamped on placemats, sweatshirts, socks, underwear(for DD), t-shirts and a bunch of other things.
Most times the fabric content was all or mostly cotton but I know that the sweatshirt & socks were part polyester.
No troubles there, either.
Good luck!