Training in one WILL rule out the others, unless you leave the first one. Of course, you can then apply to another organisation, however I have heard of people being denied due to prior organisation membership.
If you search around, you will find a number of threads/posts about the differences (I think quite a few by me, actually....), but to go through this briefly....
Bujinkan: Headed by Hatsumi Sensei, direct successor of Takamatsu Sensei, the Bujinkan is made up of nine seperate classical systems (Togakure Ryu Ninpo Taijutsu, Koto Ryu Koppojutsu, Gyokko Ryu Kosshijutsu, Takagi Yoshin Ryu Jutaijutsu, Shinden Fudo Ryu Dakentaijutsu, Kukishinden Ryu Happo Bikenjutsu, Gyokushin Ryu Ninjutsu, Kumogakure Ryu Ninpo Taijutsu, and Gikan Ryu Koppotaijutsu), the essence of which are combined to create an overall method of teaching, focused on the principles gleaned by Hatsumi Sensei from the various lineages (as well as a number of others he has trained in, such as Asayama Ichiden Ryu and Bokuden Ryu). The focus in the Bujinkan is on development of skills and flow, and more modern methods and weapons are more common here than in the other organisations. However, due to a lack of structured curriculum, there is a greater variance between the main teachers of the Bujinkan, you may get someone fantastic, or you may get the other end of the spectrum. Check the school out first.
The Genbukan: This was formed by Tanemura Sensei, former Vice President of the Bujinkan, and at the time it's highest ranked member at 8th Dan. Due to reasons that are of little importance here, Tanemura left the Bujinkan (and his cousin, Hatsumi Sensei) in March 1984, and in November formally founded the Genbukan. He spent a great deal of time furthering his studies with many former students of Takamatsu Sensei, gaining Menkyo Kaiden (full mastership) and Soke-ship (Head of system/family) for a number of systems. In the early 90's Tanemura Sensei established the Kokusai Jujutsu Renmei (KJJR) to teach the "samurai" Jujutsu systems seperately from the Ninpo-related systems. Most Genbukan schools offer both, but some only offer Ninpo. The focus in the Genbukan is on the correct transmission of the traditional schools, leading to a higher level of standards enforced than those found in the Bujinkan. There is also a very strict rule-set enforced in the Genbukan. It's teachings include the systems of the Bujinkan (from Hatsumi Sensei), as well as alternate lines for a number of the Ryu, such as Hontai Takagi Yoshin Ryu Jujutsu (Ishitani line, rather than Hatsumi's Mizuta lineage Takagi Yoshin Ryu Jutaijutsu), a different line of Koto Ryu, and more. He also has other systems, such as Asayama Ichiden Ryu, Bokuden Ryu, Araki Shin Ryu, many more branches of Kukishin Ryu, Yagyu Shingan Ryu, and more. A very traditional, solidly trained organisation. Again, though, as not every school is for everyone, check out the school first.
The Jinenkan: Formed by Manaka Sensei, Hatsumi Sensei's earliest student, in 1996, this is made up of the six primarily taught systems from the Bujinkan (Togakure Ryu, Koto Ryu, Gyokko Ryu, Takagi Yoshin Ryu, Kukishinden Ryu, and Shinden Fudo Ryu), as well as the Jinen Ryu, founded by Manaka Sensei, and focused on sword and jutte. The emphasis of the Jinenkan is the correct teaching of the schools the way they appear in the scrolls, in the correct order. Again, the standards are kept high, and the feeling is very traditional. The Jinenkan schools are less common than the other major organisations, and again one of the biggest factors will be the individual instructor. Some, such as Adam Mitchell (who posts here on occasion) explore other areas not covered in the formal scrolls (there's a great thread with a link to a clip on his approach to ne-waza, or ground fighting here), giving a bit more freedom, others will stick very strictly to the scrolls themselves. Once more, check out the school first.
Hope that helps, a look around will give a little more detail, any questions just ask.
