Redworms are the ideal worm for vermiculture because they're more tolerant of various environmental conditions; as well, they don't mind being in such shallow containers and they do consume large amounts of organic matter. You
can fashion any large plastic tote into a worm box: drilling holes for aeration (worms need oxygen as much as we do), preparing bedding, systematically adding scraps for them to eat and eventually you'll be able to harvest the castings manually. However, it could end up being more difficult to maintain and you wont be able to collect the leachate or "worm tea".
Specially made worm bins or farms are designed for the purpose; facilitating the upkeep and casting collection, and typically include a reservoir and drain for the leachate. I am hoping to get a simple altered tote style bin set up for vermiculture and soil recycling until I can get a Wormtopia after the holidays.
Whatever you plan to work with here is an excellent guide:
http://www.planetnatural.com/site/xdpy/kb/composting-with-redworms.html