Oh and as you can probably tell I am a total newbie to this whole thing
Hey, everyone was there at some point (I still am mostly :P)
does anyone have a clue as to how I can go about physically soldering or connecting all these things with the speakers and the Arduino?
You could try a Proto Shield? That's how I would do it (if I was going to solder things).
I think I might need a transistor?
Most probably, considering you are using a motor.