Sorry this is a bit late!
I've been printing my own t-shirts for years now, standard oil-based printer's ink does the trick for me - eight years and counting with no significant fade for my first black-ink print. I actually find it easier to get a good impression on cotton instead of paper when I'm not using a press - cotton has a lot more grip. The downside is that, to avoid that faded look, you need a little bit more ink than usual. This means that your lino will need to be cut slightly deeper than you'd get away with on paper, or details will fill in quickly. Just remember to use a nice, heavy book for pressing and you should get a good clear print.
Second question: if I use litho ink (recommended by my local printworks) and a really smooth paper then the only limit on printing is how fine I can cut. I'm currently finding out how steady my hand is with this piece:
http://rsthomason.tumblr.com/post/43898415743/acanthostega-lino-print-this-is-probably-the it's a bit nerve-wracking ;)