Hi again, Steve - The 20-176 antenna is a good multi band antenna if you are on a budget and it should do what you want it to do. It is rated at 108 to 1300 Mhz.
If you have room, pick up 3 of the Radio Shack 10 foot 16 gauge mast pipes # 15-863 and one house gable bracket # 15-886 as well as some 1/8 inch guy wire. Depending upon your residential configuration, this will get the tip of your antenna about 34 feet off the ground. This will increase your reception distance by roughly 40 to 50%, although there are some variables. The bottom mast pipe can be slipped over a smaller diameter 6 to 8 foot section of galvanized steel water pipe driven into the ground and left above ground by 12 inches. This will prevent the bottom mast from 'kicking out' in wind. Drill a 3/8 inch hole through the mast 6 inches off the ground - all the way through the steel pipe inside and out the other side of the mast. Use a 2 1/2 inch bolt, lockwasher and nut to secure the mast to the inner water pipe. This will also effectively ground the mast. Sounds like you may have to get a new piece of cable, so one of the common one's with low loss is RG8 which is 3/8 of an inch in diameter - much easier to work with than the larger cousin RG8/U. You will probably get other suggestions, but some Radio Shack stores have the RG8 on closeout and it is very reasonable. I recently picked up a 105 foot remnant for less than $20.00. Lightning protection for the CABLE itself is another matter. You may have to check with someone in your local electrical inspection department to see what the grounding codes are for antennas in your area. These ordinances vary from state to state and I'll leave that one up to you. In an impending thunderstorm, disconnect your cable at the scanner and place the coax connector in a tall DRY glass jar away from your radio and other electrical items. This will act as an open circut and will not look like a path to ground to a nasty old lighting bolt. BUT, that being said, I have yet to find ANYTHING that will protect a feedline in a direct hit.
Guy the mast just above where the second and third pipes join and bring three guy wires down at a 45 degree angle 120 degrees apart to eye screws in the roof (use silicone sealant around the lag) or long pipes driven into the ground at an angle away from the mast. You'll have to use the triangle leg formula for a right triangle to calculate the length of the guy wires.
The nearby woods is not an issue - but since your new mast will probably be the tallest thing close to your residence, please do the lightning protection to code. Best of luck.