Hey,
As stated a lot easier than most people think.
Here is my take on the subject:
Run the red and blk wires to the battery for power, put an in-line fuse holder as close to the battery (within reason) as possible. When running wires through the firewall make sure to avoid moving pedals, i.e. brake/clutch/gas pedals. If drilling a new hole USE A GROMMET in the hole to avoid chafing of the wires.
Mount the CB, attach the power wires red to red and blk to blk, attach the coax to the CB and the antenna, tune the antenna (this is a must for transmitting).
The coax... I am a firm believer on new coax when ever you change things around unless you know the age and abuse the existing coax has gone through. Look for Belden brand coax, not RAT Shack, the RG-58U is good to use but the best for most mobile applications is RG-8X.
As said before get the antenna tuned for low SWR this is a must if you want to transmit clearly and to the furthest distance. This shouldn't do a lot for the receiving noise but as stated moving the antenna might do some, adding a ground braid (1/2" min) from the antenna mount to the frame might (getting to bare metal at the attaching points).
As stated... there is no need to tune the CB... if you had one of the expensive units ($300, $400 and up), then the CB MIGHT respond to a tuning but most CBs get nothing out of it except more noise.
The most important part of a CB system is the antenna/coax then the CB.
How old is the setup and was the coax and the antenna in good shape when you got it ?
Luck to ya,