[This book] (http://www.goodreads.com/book/show/2217845.History_of_the_Filipino_People) is the standard one volume reading for college students and may well serve your purposes. There are myriad other works on particular periods and topics, but Agoncillo is a good introduction. Its price is ludicrously marked up on Amazon though, to about 10 times what it costs for students in the Philippines. I'd recommend borrowing a copy from a library if you can find one.

Another read you may want to check out because it's such a cultural touchstone is the novel Noli Me Tangere by Jose Rizal, the Philippines' national hero. It was written late in the 19th century as commentary and criticism of Spanish colonial society. Rizal was executed by the Spaniards essentially for his writings, of which his novels were a pivotal part. Originally written in Spanish, it remains mandatory reading for all high school students in translation and is thus a common and cultural touchpoint across swathes of the diverse Philippine sectors.