In terms of getting my designs printed by someone else, I will have to think largely about cost. They will definitely need to be cheap to print, both because I don't have a lot of money and to enforce my point to designers and printers that sustainable print can be cheap.
I have found a printing company that prints on FSC certified stock and is really cheap. Although for short runs, there isn't much choice on stock type or size and nowhere on the site does it mention the printing inks being eco-friendly.
Pureprint are a carbon-neutral printers based in Sussex. G F Smith is a past client of theirs. I would be printing digitally, which I would have to ring up for a quote.
I Dress Myself, an eco-friendly screen printers has a lot of very useful information on the different types of ink to use. Water based inks are best as they don't include chemicals that are harmful for the environment, neither do they require solvents to clean the screens after, just water, which is friendlier.
Wicked printing stuff sell Permaprint premium water based paper inks. They aren't massively expensive, but they do only offer a limited amount of matt or glow colours.