A couple of things. Looks like there are two areas where you plan to place only a single speaker. Now, if you're really playing '50s music, you might be fine, but if you get into the '60's, you'll have an interesting problem. When stereo burst on the scene, a lot of music was mixed so that the fact you had stereo was unmistakable. The would place vocals on the left, band on the right (a lot of Beatles stuff was released this way), so with one speaker, you're going to miss something pretty important. You'll either have a a-capella vocal solo, or a karaoke band only. Even out to the latter half of the 1960s this was still being done. The Mamas & Papa's classic "Dedicated To The One I Love", played in stereo, but with only one speaker becomes either just the Mamas, or just the Papas. Not good. So, if you really want only one speaker somewhere, you'll have to make sure that your stereo music source is somehow mixed to mono before you hit your amplifier.
I haven't heard the speakers, they look ok, nothing special. You might consider one of the T-power amps in place of the Pyle, and save yourself some money. I have one of these:
Amazon.com: LP-2020A+ Lepai Tripath Class-T Hi-Fi Audio Mini Amplifier with Power Supply: Electronics
It's used for background music, and computer sound only in a non-critical location, seems to work just fine. Check the price too. You can buy two of them and have independent volume controls for at least two pairs each of your speakers, no piggy-backing required. You can mono the source up at the input using Y cord.
As to sources, if your bro will ever get into computer audio (which he should, he'll love it), using iTunes (free) and his music, you can wirelessly stream audio to an
AirportExpress or two, feed those little amps with it, and you can have streamed playlists all over the house with central and independent volume control at the computer. It nudges your budget a bit, but adds a whole lot of functionality.
Sonos stuff will be outside your budget significantly, but adds simplicity of setup, iTunes library playback, and individual control of what plays in each zone, with the option for "party mode" to play the same thing everywhere. Much more expensive, but really easy to deal with.