They vector file should be fine to send to most printers to get your t-shirts made.
For screen printing, if you have a raster file, the printer usually recommends that the design be at least 300dpi at the size you want it printed. The dimensions would be up to you (how big or small you want the design printed).
yea, everything I've read has said 300dpi. As a side note, my first design came out a little jagged on the transparency <sp?> negative. The edges were slightly "fuzzy" as well when it was put on the screen, but you can't tell at all on the printed shirt. I think that a one color design affords you some leeway in that regard.
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