Organic cotton sheets from Target (better colors) and Kohl's are probably the most affordable. West Elm is a little more expensive, then you have high end which would be Coyuchi (top on my list if i can ever justify spending $168 on a set of sheets), Gaiam, Under the Canopy, Loop, Plover Organic, even Pottery Barn is in this price range, but i would go for the eco friendly brands instead.
I don't know if Target has organic pillows, but you could search online. The best website for bedding is thecleanbedroom.com, most of the things are pricey, but it can serve as a great guide and you way just find a few things worth investing in!
Try Ikea or West Elm, they may have some 'alternative fiber" pillows like down alternatives and such, which may be less expensive. instead of going for full on organic pillows, get organic pillow protectors, they will cost a lot less
I am buying my first house (yay!!) so I think now would be a good time to invest in some new organic bedding. Thanks for the tips! I am having a hard time making a decision about a mattress. I have been looking at Essentia(comparable in price to Tempurpedic). Does anyone have personal experience with any organic/memory foam mattress'? I'd appreciate any advice.. thanks!