I have recently become intrigued with the history of the early Islamic state after the demise of Mohammed. In particular, I want to know how a civil war ensued within the state over what I believe to be a struggle between two factions on where to locate the capital of the state. Moreover, related to the topic of the location of the capital, why were Mecca or Medina not considered as viable options?
Also, I've read slightly more about the time period recently and learned about the emergence of a third major faction called the Kharijites. I have not come across much in the way of an explanation as to why they emerged and how they came to have such extremist viewpoints. Lastly, I've been interested in how the early Islamic state inherited so many problems from rapid expansion within groups of disparate peoples, experienced multiple civil wars as a result, yet still managed to keep expanding afterwards.
Marshall Hodgson's The Venture of Islam and Jonathan Berkey's The Formation of Islam are probably your two best bets for early history.
As for the Kharijites, W.M. Watt's the Formative Period of Islamic Thought will explain the emergence of that group.
I would advise you to slow down a little bit however, as the current scholarly consensus is that these early battles and developments, while a major part of the narrative for later generations of Sunni and Shia did not witness the emergence of those groups as fully fledged entities. So we're hardly dealing with "three major factions" in the first century after the death of Muhammad. Which is why so often you encounter terms like "proto-Shia" (or better yet, "Alid supporters") and "proto-Sunni."
As for expansion, the internal strife halted expansion, which led to greater internal strife. Expansion west was halted at Tours, and east at Talas in a 20 year period immediately before after the Abbasid revolution, respectively. Within a century the fracturing the empire picked up pace rapidly as local dynasties gained control.
The capital during "The first three caliphs" reign over the islamic state, the capital was in Medina as it was where Islam was first established. After the demise of the Uthman, Ali (a.s.) was given leadership. Now as "the fourth caliph" Ali ibn Abi Talib (a.s.) was met with alot of hostility and pressure to find the uthmans killers. A party of people who gained some support were disgruntled with the amount of time He was taking to catch the killers marched to bagdad. As the first civil war was breaking out, Ali (a.s.) decided to move the seat of the caliphate to Kufa for strategic place to defend the caliphate from the civil war and also muawiyahs empire in todays syria. Theres a good read in the link below that explains why he moved capital.
http://www.bbc.co.uk/programmes/b00c5xzc
I cited this In Our Time radio program in another answer. I really love this program. The premise is that a moderator leads a discussion between three professors from the London area or one of the Oxbridge institutions.
All of the programs can be found on iTunes, but if you look at their website you can find introductory bibliographies with works selected for a variety of audiences. You might start with one of those for the Rashidun.
After the Prophet: The Epic Story of the Shia-Sunni Split by Lesley Hazleton and Heirs of Muhammad by Barnaby Rogerson are both good books on the subject that are written for a non-academic audience.
For information on the Kharajites specifically I recommend "Ninth-Century Muslim Anarchists" by Patricia Crone in Past and Present. I don't have a citation right now, and it might be behind a pay wall, but I'll try to track it down tonight.