The only comprehensive book that tries to tackle this that I'm aware of is Michael Oren's Power, Faith, and Fantasy: America in the Middle East: 1776 to the Present.

I have to admit I haven't finished it, but it's likely to be as good an introduction as any other.

Beyond that I'd be happy to suggest other books, but they tend to be either A: less focused on America than on the region as a whole, or B: from America's perspective but focused on a particular time, region, or conflict, i.e. histories of the American-Israeli relationship, or the origins of the War on Terror.

In terms of free, organized, online resources, I can't really think of any that are comprehensive, but I can point you towards resources that I use and read. I would suggest having a look at articles and topics that interest you from The Carnegie Endowment for International Peace, The Atlantic Magazine, and the Brookings Institution. It requires a subscription, but there also quite a lot of introductory history articles like this published in Foreign Affairs Magazine.

Edit: I'm also happy to take any questions you might have. For what it's worth, despite some kind of American presence in the Greater Middle East going back practically to the founding of the country, I'm not sure that I would put too much weight or interest on events before 1900. Or when you say "how the current political climate has formed," if you're talking about the political climate in the Middle East, I'm not entirely sure I would too much weight on the United States at all.