I good place to start would be to take a look at the Dharma Trading Co. catalog. They specialize in dyes and how-to books and carry lots of wonderful products.
A lot of quilters are heavily into dyeing fabrics, both cottons and silks, so you might ask around in some of the quilting discussion groups and Web sites on the Internet. I think there are some discussion groups just for sewers and quilters who dye.
Years ago I knew a gal who did lots of fabric dyeing--again mostly with Dharma products--and the fabrics and colors were gorgeous. She did lots of purples. There are products and "dye setters" that will make the fabrics colorfast if appropriately applied. It's a separate step.
One thing you will need is large pots and pans and spoons for the dyeing--you don't want to use this stuff for cooking. But you can find these things at the Goodwill.
I'm sorry I can't be more specific with advice. I've never much gotten into dyeing fabric. I did a little experimentation years and years ago but can't for the life of me remember what products I used. My few subsequent flings with Rit Dye have been disappointing. But I do know gals who've dyed some gorgeous fabrics and garments and I think it's worth a try. I'm always very disappointed with the limited range of colors and hues in store-bought clothes, especially when dyes in every gorgeous color in the rainbow are available.
Be sure to upload pics if you dye any shirts! Good luck!