Well, like most things,men, wine, cheese... older is better.
Screen printing is just the best. It looks great, you know the quality you will get and if you do it with th right materials your stencils can last forever!!!
They will never be obsolete is what I mean.
They are a little more work, but like most things, fruit, message, se...oh, erm...the harder the better.
You would either have to buy a screen or make one, I suggest making one.
Digital is iffy. Programming is WAY expensive, or if you don't want to buy the programming, getting someone to digitalize them can be pricey. I charge about $50/hr to digitalize depending on the design.
And your print might be of low quality because its coming from a printer. Also, sometimes I find printed images thick and cakey...and they crack and peel and fade and flake when they age.
Defiantly screen print.
Cotton and Polycotton should work fine, but, if you don't already know, the mesh of the screen you're using will really make the difference in clarity of the print. A higher mesh gives you higher 'resolution', so if you're design is complex it'll be clearer. Lower mesh counts are great for bold graphics, but anything complex would require a high mesh count for detail.