If your intention is to build from scratch, you'll need a good amp circuit and three effects pedals, of course. The challenge is that each needs it's own power source. That requires four 9v batteries, or four individual 9v adapter inputs and wall warts. Kind of "busy", if you see what I mean.
That doesn't mean it can't be done.
The resulting amp it seems you're after is identical to what is found on, for example, a Roland Micro Cube, which has effects, etc. But amps like that are set up to use one effect at a time, not multiple ones, with the exception of a distortion/overdrive switch that can be used along with, say, reverb, or delay simultaneously.
A decent amp circuit, like the Guitar Fuel MAH-5 (a 5 watt unit which has 5 different amp voices like clean, tube, rock, metal, overdrive) runs about $70 on eBay. Other amp circuits like 2 or 3 watt versions run from $25-40.
Effects pedals can be found fairly cheap, if you do the homework and shop around.
Another option is to source a Micro Cube (or other similar amp), remove the internals and install into your own hand made cabinet. Then to use the Polk speakers, use them to make an external speaker cabinet. Add a "line out" jack & switch to the amplifier so you can either use the amp's speaker, or divert the signal to the external cabinet for a different sound.
Good tips from Farmer Ted. I would only add that a daisy chain is an option to combine your power source.