Hey MKube and welcome to the forum.
I'm surprised that you did not do much research before you asked your question. There is volumes written on this subject on the web right now.
I'm not as well versed in this subject as I would like to be - but I will take a stab at your question and answer it as good as I can.

I think the ladder line you are talking about is 300 ohm and not 450 - but I am not trying to nitpick your post.
My opinion is that most communications grade wire is 50 ohm because 50 - 52 ohm is about the load that the wire carries and the engineers when they design a communications receiver / transmitter uses 50 ohms as the basis for their design.
Now you have to understand that a antenna is a resonate piece of equipment and is designed for one center frequency.
For the purpose of example - lets use your CB radio - which is 11 meters or 27 mhz. is about 434 inches at 27.205 mhx - channel 20.
There is not a lot of disparity between channel 1 - 26.965 and channel 40 - 27.405
One antenna cut to 36 feet long will service all the bands in that frequency wavelength.
At the same time a antenna cut to 22.5 feet will also work - as a 5/8 wavelength.

Now as the frequency changes - so does the wavelength.
So does the load on the feedline - do up and down in resistance.
So at 27 mhz the feed line is balanced at 50 ohms and at 50 mhz the load on the wire might be 400 ohms.

The receiver doesn't really care if the load is 50 ohms or 500 ohms - just that you properly try to match the length of the antenna to the length of the wave length you desire to receive.
I had an article here someplace that explained that the RG 6U Quad Shield actually makes a better coax - because it has a lower loss rate as per loss per a foot - while maintaining a good shield on the coax from top to bottom.
Without the shield - the ladder line becomes one big antenna - as soon as it comes in contact with a metallic object.

So the goal is to use the RG 6 wire and to use a good antenna and if you desire to receive frequencies higher then 400 MHZ to use some type of pre amplifier to compensate for line loss.
If your main goal is to receive 2 meters - 146 mhz, which seems to be real popular right now - you can repurpose a old television antenna and a antenna rotor to aim the antenna in the desired direction to receive as much signal as possible.

If you want to receive the lower ranges of Ham Radio, the antenna is going to need to be larger then the home television antenna and will not need any type of amplification - due to the fact that the lower ranges do not have as much loss per a foot of coax as does the higher frequencies.

Here is some information about frequencies being used by general radio right now.. http://flashoffroad.com/radio/radio_frequenc.htm
Here is a frequency wavelength calculator - http://www.csgnetwork.com/freqwavelengthcalc.html
Here is a AARL link for frequencies of Ham radio - http://www.arrl.org/files/file/Hambands_color.pdf
http://www.arrl.org/frequency-allocations

Remember to start out simple and keep it affordable.
Shortwave radio listening can be a lot of fun.