The all red wire should be positive, there should be a red/white wire also..thats your ignition wire that runs up to the battery i think but im absolutly positive about the red/white but it should be igntion..(it is on most 50cc's not sure of the 150's)if you wire it thru there when you turn the key on it will power the radio..if to the battery you will always have power connection
i would actually take the extra time and using zip strips to mount the wires along your framing and go directly to the battery with an in-line fuse first. Im not sure how much the wiring of your scooter can withstand as far as heat so just in case i wouldnt go splicing. either way you do it make sure you use an inline fuse. you can use any metal that touches the frame for the ground as long as its a clean connection.