You should note that you will spend MORE to build this amp than if you just bought a reasonable used Japanese receiver or integrated amplifier from your local Craigslist or from eBay. You can get a 50 watt per channel amp for around $100 -including shipping! - if you shop around. You can't build a high-quality amp for this little money.
For example, on eBay right now is an NAD 3225PE integrated amp for $45 "buy it now" + $15 shipping! So, for $60 you have all the power those Pioneer speakers need, PLUS a preamp with a decent FET phono stage! NAD products of this vintage tend to sound pretty good, a cut above the Pioneer / Sansui / Kenwood products in this range. For $60, you really can't build very much. The chassis alone could cost more.
But if you are determined to build something, there are lots of nice PCB's for small / moderate size amps on ebay. You can buy a PCB for a good quality class A amp and then order the parts from Digi-Key or Mouser. This would give you experience in navigating parts purchase.
I have had good luck buying stuff from Jim's Audio, which is an eBay "store" - http://stores.ebay.com/jims-audio-store
For example, they have a design for a 25 watt / channel class A amp similar to Mark Levinson designs, see eBay item# 320385762535. You can buy the PCB from them and build it yourself. 25 watts / side would probably sound nice on your Pioneer speakers which are probably pretty efficient (i.e., they don't need much amplifier power to play loud.)
"Class A" is a technical description of a certain kind of amplifier that typically has somewhat lower distortion than other types. Class A amplifiers are often thought of as a "better" amp design, more or less. (Your mileage may vary - there are some very good Class AB amps out there! And there's always class D and other switching amps.)
The class A amp would also work nicely with your NEXT pair of speakers, too, which may be more revealing than these Pioneers.