The way I understand the process of becoming a Vaizard, is that Hollow and Shinigami are two sides of the same coin. Basically, every soul has the potential for both of them. Whether they were at peace when they died, and went to Soul Society, or they became a tormented soul would determine if they became one or the other. From there, you have two choices, as I see it. You could either start as a Hollow, get purified, and sent to SS, and become a Shinigami, or you could bypass all that, and start a Shinigami. Either way, you would eventually want to - somehow - begin giving into more carnal desires, becoming more violent, more instinctive, essentially letting the Hollow side take over. From there, you let it get out of control, to the point where you become more Hollow than Shinigami, and then bring it back under control, and learn how to use the Hollow side through Vaizard abilities.
These are only my personal thoughts on the matter, and it's very likely that they don't make sense, in which case, I apologize. Also, if anyone else says otherwise, their answer takes precedence.