Is there a difference in dB loss between connectors?
Use the connector that matches what you're connecting to whenever possible. Any adapters will most often more than wipe out any gains by using a "low loss" connector on the cable that doesn't match what it's being plugged into. If your antenna uses an "F" connector, this should be used there and if your scanner uses a BNC, then that's the best choice on that side of the cable. There's nothing that prevents you from using different connectors on the same cable (assuming that you get ones designed for that type of cable).
Since it sounds like you're doing a totally new installation, you're probably in good shape to do it right with minimal compromizes.
Without knowing specifics (like radio, antenna, frequencies, etc.), a good rule of thumb would be to use LMR400 for the coax and "N" connectors when possible (like on your lightning supressors). Be sure to seal all connections that are exposed to prevent water from getting into the cable. Since LMR400 is quite stiff, be sure to only have gentle bends in the cable. I often recommend that you make a patch cable (keep it short, 6 foot or less!) using flexible cable like RG-58, RG-6, etc. between the end of the LMR400 and your radio. This will reduce strain on the connector on your radio.
Good luck with your project!