I usually always do my designs up in Illustrator. Producing a vector graphic for seperations is the best because you always get sharp clean edges and lines. I have screenprinted one pixel lines off of vector art and had it come out as clear as a bell. You would never get those results from a bitmap image.
I think whether you use rastor or vector images depends on the type of graphic you're thinking of getting printed. One-color or simple text designs are definitely good in vector format. Photos and other kinds of art are usually done in rastor (Photoshop), which I use mostly and never had a problem with it. (Of course, I currently use cafepress which prints in full color, but many screen printing places will do color separations, I'm pretty sure.
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