I do not know your background so here is a bit of theory: AB power amplifiers are supposed to give the amplification efficiency of a class B amplifier and also the reduced distortion of a class A amplifier.
Other aspect of an amplifier design - mainly to reduce distortion is to provide a slight negative feedback. - there is a need for biasing resisor for the transistor base and collector. Analog theory is unfortunately very complex involving mathematical modeling and I experienced that very few of my friends during the 4 year BS course actually understood it (not trying to discourage you - its a fact).
The reality is that even after I understood this complex theory, I was not able to successfully design a single commercial grade amplifier. Not just because of my laziness, there are factors like variation from piece to piece of a BJT (yes! that what these little transistors are called - Bi Junction Transistor)
Fortunately, unless you are planning to use valves (which per circuit you are not), thanks to the more recent techniques developed, Class-T can give much better efficiency and surprissingly great sound.
Check this link out for this very inexpensive class-T amplifier that blew me away when I heard it for the first time. Unfortunately the company closed down and copycats are the only ones available but if the underlying principle has not changed, I wouldn't think that the sound quality would change much:http://www.ebay.com/itm/NEW-Tripath-TA2020-20W-Class-T-Digital-Audio-Amp-Chips-/120751783917?pt=LH_DefaultDomain_0&hash=item1c1d5dffed
You should be able to get the data sheet on the internet that will guide you on how to use the chip. If you do not want to assemble it, just buy a readymade amplifer for around $20...now THAT is cheap!!