It also depends on what (European) language you are native or good at reading. If you can primarily read only English, the following two classics are still his recommended biographies to go at first:
At the turn of the 20th and 21th centuries, however, the important document collection of Sicilian kingdom under Frederick's reign had been published, so both several German and Italian scholars (I know little about the latter, though) have published biographies (as well as essay collections) on this emperor, called also 'wonder of the world' even by his contemporary people.
Among others, I'd especially recommend:
There are three major ones in English:
Ernst Kantorowicz, Frederick II: 1198-1250, which is actually originally in German, but was translated into English by E. O. Lorimer (Ungar, 1931). Kantorowicz presented Frederick as a sort of idealized mythological Germanic hero, which is a bit strange to read these days, 90 years later. Kantorowicz was criticized for his credulous acceptance of legend as fact and his lack of footnotes. It was an enormous book though, full of information, and was so immensely influential that it basically ended any further discussion about Frederick until...
Thomas Curtis Van Cleve, The Emperor Frederick II of Hohenstaufen, Immutator Mundi (Oxford University Press, 1972). Van Cleve depicted Frederick as far ahead of his time. Frederick was somehow, almost magically, able to move between the secular and ecclesiastical worlds like no other medieval person, and yet was somehow also above it all, as if he had travelled there from a more enlightened future. This is in contrast to Kantorowicz's portrayal of Frederick as if he was from a heroic, idealized past - although the ultimate conclusion is similar, that Frederick was a unique monarch and almost out of place in history.
A bit more recently there is also David Abulafia, Frederick II: A Medieval Emperor (Oxford University Press, 1992). Abulafia sees Frederick as a totally medieval ruler, with medieval mindsets and acting in ways that are completely typical for a medieval person - unlike Kantorowicz or Van Cleve. But like Kantorowicz's book, there aren't really any notes, which makes it a bit difficult to use for academic purposes.
There are some newer works about Frederick but nothing major in English, as far as I know (there's one in Italian by Marcello Pacifico, for example). So for now Van Cleve and Abulafia are probably your best choices - especially Abulafia, if you're just interested in Frederick's life and aren't using it for scholarly research.
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