There is another approach that you might consider.
At SBN - The Scannerbuff Network - we use a Diamond MX2000 and MX3000 triplexer reversed. This gives tuned ports on 30-100, 100-175, and 200-1000. We use a separate antenna for low band (CHP), VHF (CALFIRE and others) and UHF or 800mhz. This is obviously not for a handheld installation
But for a base it kicks the snot out of a "scanner" antenna. Because these are tuned ports images and birdies tend to disappear. But because we are using gain antennas tuned for a specific band we cannot run an amplifier and sometimes have to add 3-20dB of attenuation using F barrel attenuators. The net result is still better than a discone or other all-band antenna.
There is nothing wrong with using F connectors. They are just BNC connectors in a different form. I use compression connectors by Ideal and have jars of connectors, coax strippers, and the compression tool. They give a solid connection that is waterproof. For serious feeds I use LMR-400 and UHF or N connectors, but I also use RG6 Quad shielded 75 ohm cable. Up through 512mHz its loss isn't bad. Climbing towards 800 it becomes questionable except for strong signals. I also use CATV splitters good though 3GHz and feed 8 radios. The scanners automatically choose the best antenna (path of least resistance.)