For promotional material (like tee shirts, bumper stickers, banners, etc.) it's always best to use a vector based image. Photoshop creates a raster image, which is why if you try to upscale (or even downscale) anything within Photoshop, it'll get blurry or pixelated (or both). With a vector image, even if the printer you are using does not accept vectors, you can output to a hi-res transparent PNG and just use that.
However, it can be hard to create more advanced/detailed logos within Illustrator.
I've done screenprinting before but never for my site. We've thrown the idea around but since we are a fan site, we could run into copyright issues--though I don't think it'd be much of a problem as long as we didn't sell them for profit, just for giveaways or something. Might make it my summer project to do a quick run of shirts--which, btw, if you have a simple logo and like DIY,
Lifehacker did a great guide on it.