For an intro to both, Desmond Seward's The Monks of War (Penguin, 2000) is a pretty good, and includes a look at the Hospitallers and the orders that formed a significant part of the Spanish Reconquista. It also has a rather useful section on their modern survivals, if you'd ever wondered what the present Knights of Malta did with themselves these days.

For the Templars alone, Malcolm Barber's A New Knighthood: A History of the Order of the Temple ( Cambridge, 1994, 2013) is more in depth. It's also (in part) over here

OP might have difficulty in finding modern English translation of the primary texts.

At least I could previously refer to Nicholaus von Jeroschin's the Chronicle of Prussia (Eng. trans. Mary Fischer) when I wrote an answer to Sex in the Teutonic Order?.

The work in question is originally commissioned by the Master of the Teutonic Order as a history of the conquest by the Order in early 14th century in form of verse-style chronicle (in Middle German), so this English translation might not be so readable as William of Tyre's.