For Arabia generally, Robert Hoyland's Arabia and the Arabs from the Bronze Age to the Coming of Islam (2001) is a good overview. For a book covering the complicated world of northern Arabian politics in the sixth century, Greg Fisher's Between Empires: Arabs, Romans, and Sasanians in Late Antiquity (2013) is excellent. For southern Arabia and more specifically the conflicts around Yemen at the same time, Glen Bowersock wrote his The Throne of Adulis: Red Sea Wars on the Eve of Islam (2013) for a general audience, so it is very readable and thus highly recommended. I'm not sure what would be a good book for the Hejaz region, where Islam was born (probably). Perhaps reading Patricia Crone's Meccan Trade and the Rise of Islam (1987) would be useful, even if her core thesis is unconvincing, since she did a fantastic job demolishing the view that Mecca was a hub of international trade.

For the political situation during and after the rise of Islam, Fred Donner's Muhammad and the Believers: At the Origins of Islam (2010) is a readable introduction to the topic, though you might find his thesis unconvincing; check out Hugh Kennedy's The Prophet and the Age of the Caliphates: The Islamic Near East from the 6th to the 11th Century (2004) for a more traditional interpretation. This period also can't be separated from the events of the Arab conquests, which is best covered by Robert Hoyland's In God's Path: The Arab Conquests and the Creation of an Islamic Empire (2014). Since you also seem to be interested in the Middle East as a whole, an up-to-date overview of this region's history can be found in Peter Sarris' Empires of Faith: The Fall of Rome to the Rise of Islam, 500-700 (2011).