Greetings, most scanner antennas are rated at 50 ohms, and a good quality coax is most often available in 50 ohms... its a pretty good match. The discone antenna you will be installing is in the same family as the 1/4 wave antenna which was designed to perform best for the wide frequency bandwidth. You should most likely experience 0 db of gain with a discone antenna and it will operate best between the frequencies of 120 mhz through the 1300 mhz range. If the discone you have has an additional single vertical whip antenna attatched to the top of it, it should pull in signals from around 30 mhz up to 1300 mhz. I feel the discone is the best all around all band scanner antenna for the money.
One thing that you have to remember is, there is NO substitute for antenna hieght. I dont suggest mounting a discone or any antenna under the roof, or in an attic, unless you are trying to conceal or hide the antenna from the nieghbors. The roof acts as an obstacle. For the same reason you wouldnt want to mount your new antenna up in a tree secured to some thick - heavy limbs or branches. Its in my opinion to mount the antenna on a sturdy grounded mast, approx 10 to 15 feet above the peak of the roof. Please note that the antenna is designed to work best in an opening, free of obstacles. The higher the better when it comes to line of sight for best reception, but to pull in weak signals, you would have to go up as much as 100 or even 500 feet for some distant line of sight signals. Just be sure to clear houses on the block, and take note of the hieght of close proximity trees. Raising the antenna up on a mast any higher than 20 feet above your roofline is only going to yield you trivial added reception with-in your receiving range, and prove to become a dangerous installation.
Back to the 50 ohms coax... usually the average scannist says he gets by with radio shack cheap coax. That might work good for him if he has an extremely short run, as if run out of his bedroom window and to the antenna mounted 6 feet away to his fire escape. RG8 U or Belden 9913 is really good stuff. The 9913 is more expensive, but not too bad if you require a run of about 30 to 50 feet. I use the Times Microwave LMR-400 coax myself, its real thick in diameter, and sometimes difficult to run, but its worth the price to me to utilize a quality coax with quality shielding as not to develope a signal loss. If you do go this route, LMR-400, have it custom made (hand-made) by a professional. This will ensure that the ends, (connectors) are properly installed, with flex shielding shrink to help eliminate stress, and that you try to obtain the true silver connectors. Thats the route I took, and my connectors never let me down. A PL-259 connector at both ends should work fine, with a BNC adapter on the end to mate up to the scanner... if the scanner has a BNC connector that is. RR has teamed up with Scannermaster, and Scannermaster could be a great source for the coax at competitive pricing. Remember, this reply to you and anyone who reads it is basically just my own opinion, and I have sent you this reply as a helpful hint on what has worked for me the best in the past. Be careful when installing any antennas, masts, and coax. I do believe that the thick diameter of LMR-400 coax can accept compression fittings, and regarding differences between 50 and 75 ohms, it shouldnt hamper your particular installation... I would just go with matching the same ohms rating of the coax that you choose to the ohms rating on your discone ( I believe it to be 50 and your scanner is probably rated at 50 ) if it tells you what its rated at in the owners manual in the specs. Happy monitoring, your friend Kevin.