Before I get too far into this.
I was wondering how exactly to connect the circuit straight to a speaker.
The plans show wiring to an output jack for a speaker cab, but I'd like to just wire it to a speaker.

Do I just take the wires like I would to the output, but just connect them to the speaker?
And other speakers I've seen have little connector things on the ends of the wires. Is there a certain wire to use with these or can I just pick some up at radio shack?

heres the link
Yes, just go straight to the speaker instead of the jack. You can use those speaker clips or you can just solder them right to the terminals.
Yep, just go straight to the speaker. Ground wire to the negative terminal of the speaker, and output wire to the positive terminal. As for wire, I like to use solid core stuff like they sell at radioshack. For guitars I'd use braided but for stuff like pedals and this type stuff I find the solid core to be easier to work with.