Right, "Rom" means "man" (in the sense that one might speak of
mankind) but can also mean "male" or "husband" depending on context. "Roma" is the collective name we give ourselves. "Romani" (sometimes with two "i"s) can be used instead of "Roma" but more commonly refers to the Romani language. Sinti, I'll get to in a second. Our language is shared... to an extent. Again, I'll come back to that in a second. The word "gypsy" is controversial. It's patently inaccurate (it's derived from "Egyptian" from the Middle Ages assumption we were from Egypt) but some find it offensive and some don't. Personally, I don't find it offensive. "Gyppo", however, is roughly akin to using the n-word to a black man and a really good way to start a fist-fight.
Right, potted history is that we originated in Northern India. We left India sometime around the Ninth century. According to current theories, the Roma left India in three distinct waves which give rise to the great clans: Roma (yes, also used to refer to us as a people, it's confusing) who travelled among central Europe and the UK; Sinti (Germany & Austria) and Kale (Spain). We're also related to the Dom (MidEast and Turkey) and Lom (Caucasus) but whether they're simply clans of the Roma people or distinct but related ethnic groups depend on who you ask. Personally, I tend to think of them as two more great clans because that gives us five and that's a psychologically appealing number (yes, sometimes I can be that shallow). Each great clan is sub-divided into smaller clans such as the Rom/Romale, Kalderesh, Lovari, Gurbeti, etc. And the smaller clans are subdivided into families. I am of the family Nock, which is part of the clan Rom/Romale, which is part of the great clan Roma. To add to your confusion, the Roma of different nations use different terms for themselves. Here in England, the preferred term is "Romanichal".
When we left India, we had a shared language and to some extent, we still do. However, in the intervening eleven hundred years, the language has evolved into seven related languages and numerous slightly different dialects. According to Ethnologue, the most widely spoken are the Vlax, Balkan, Carpathian and Sinte. To make all this even
more complicated, Romani has thousands of words appropriated from areas we travelled through or settled in
and we're traditionally an oral culture, it's only very recently that we've started writing down things like our history. The result is that a Kalderesh and a Sinti could communicate enough to get the basic gist of what each was saying but would lose finer, more subtle meanings.
For books, I can't help you. However, I've heard good things about "I Met Lucky People" (Yaron Matras). I can direct you to several websites though:
InOtherWords have a pretty good overvie (
http://www.inotherwords-project.eu/content/project/media-analysis/terminology/terminology-concerning-roma)
Wiki has a pretty good account of our history (although it differs from our folklore origin myths):
http://en.wikipedia.org/wiki/History_of_the_Romani_people
ScottishGypsies is a pretty good info source, just be aware that it has a stated area of focus:
http://www.scottishgypsies.co.uk/
Finally, GRTHM have a fair bit of decent info:
http://grthm.natt.org.uk/index.php