You want a smart phone, then, built for android and easily rootable… but I don’t own a cell phone so I can’t really recommend any specific model, sorry. A cheap used no-contract phone with wifi, put CM on it (and you never actually have to use it as a phone unless you feel like it) and it’ll fit in your pocket. Although actually a Nexus seven fits in my pocket, as does the nook, because I am largish.
One of the problems of doing the research is the plethora of how-tos. Every time a new device or version of CM or version of Android comes out, three more how-tos come out. You drown in information until you find a how-to that not only speaks in language you understand at an appropriate level of detail for your understanding but also fits the device and version you have.