"First though, my posts will always have deficiences due to two main
reasons:
Haste
Ignorance"

No problem; Haste and Ignorance are our muses...

"Do you have any recommendations for books that are accesible and
readable about this history?"

There are lots of books I could recomend. Probably the best interesting and
accesible historical works that should be available are three books by John
Julious Norwich; Byzantium: The Early Centuries, Byzantium: The Apogee, and
Byzantium: The Decline and Fall. He reciently came out with a one volume
summary of all this, too. I can't recall the exact title. For the middle
Byzantine period I also am particularly fond of a book by Warren Treadgold
called The Byzantine Revival. This one might be harder to find; good
university lybrarys might have it. But that, and another book by him
(Byzantine State Finances in the Eighth and Ninth Centuries) has a lot of
good info for DMs and players on how to set up and run a state, what kind
of income a "real world" midieval country could manage (roughly 3 million
Nomismata, or G.P, per year), etc. Eventually I've got to write my game
translations of this up for publication in Dragon or somewhere (a la
Catherine Kurt's old article a long time ago on administering a midieval
estate/castle. I think that one was called "who lives in that castle?" and
was in, I think, issue '89. Time for a new varient. Ever notice that most
published kingdoms, like, say, Cormyr, represent more Renaissans
Monarchies, and not so much midieval fudalism? Well, I digress...)

But here's one by an author you'll all have heard of, a one volume history,
which for a thousand year empire is kind of quick, but he does a good job
(of course), Byzantium: the Forgotten Empire, by Issac Asmov. That's
probably the 1st history of Byzantium I ever read (not including stuff I
read in histories of the Crusades, which is what got me started down this
path). It is an easy read, and is a good into. So, actually, if I didn't
know much about the history of the Eastern Roman Empire, and wanted to find
out stuff quick, I'd start here. But, IMO, it is a poor source of game
inspiration, because of it's brevity; everything goes by so quick, not much
time for the detail and individualization that can inspire game ideas, and
most titles and names etc. are translated into english, or, at best,
latinized stuff that you're probably already familiar with.

For related, fictional stuff look for books by Harry Turtledove. He's got
three seireses (my spelling is not good) set in a fictional "Videssos"; 1st
one sets up a couple cohorts of a Roman Legion geting magically transported
from the Gaul of Ceasars time to what is, in effect, their own future
(though it is so different, they never realize it...) and basically tells
the history of Manzakurt and the rise of Alexios Comenos, with some twists
(with some magic thrown in, etc; interesting villian, uses the history as a
source of ideas). 2nd set of three books tells the story of the rise of
Basil I Makedonion, but with stuff from the reign of John I Tzimicies
thrown in. 3rd set of books (the last of which is not out yet) tells the
story of the Emperor Heraklius. All are good, and, IMO, they are
particularly good as a source of materiel & ideas for Birthright, 'cause
they deal with individual heros who by their actions direct the fates of
nations. Got some good battle descriptions, too, and magic; well, lets just
say you don't have to be casting fireballs to throw armies into confusion.

What does this all have to do with us? Well, if you're a DM (or even a
player) it is a good source of names, titles, ideas, etc. that almost no
one else will be familiar with. Ok, the Mayor of Masetiele, for example;
he's called an Eparch. What's an Eparch? Well, a kind of mayor. But not the
same ol' title. I got all kinds of titles etc. out of stuff like this.
Someone, someday, should build a fantasy empire in an AD&D world that
reflects this stuff (though, if anyone has "The Time of the Dragon" for
Dragonlance, and looks at the map for the Minoutar League, many of the
place names; towns and such, are E. Roman/"Byzantine". But the League's
culture et al isn't).

I could go on and on, but I'm probably boring everyone already...