I have an Ultra-wideband 25 to 3000 MHz Discone antenna 20 foot above root, and need 75feet total cable.
Do you really need an antenna that has that wide of a frequency range? An antenna is quite frequency dependent so the wider the frequency range, the lower the gain you'll generally get from that antenna. If you only listen to stations in a narrow frequency range you'll have much better performance from an antenna that is specifically designed for that range. Just because your radio covers that wide of a range doesn't mean your antenna must also do so. Think of this, your car is designed to run on the millions of miles of roads, but chances are you only drive on a few thousand of them.
Gain dBi: 2 (nominal), Type N connector.
OK, translating this to normal gain terms, you have a unity gain antenna so you aren't gaining any performance from the antenna besides it being placed in a better location.
This is going into a 50 ohm input SDR receiver (no transmission).
Since there is no transmitting, you can basically ignore the radio's input impedance so long as you don't get too far away from that 50 ohm mark (75 ohm will be fine, 450 ohm, not so much).
What is the best cable type for this setup?
Since you never said what frequency range(s) you actually listen to, we can only give a very generic answer to match the frequency range of your antenna. Be aware that that 3000 MHz top end will force our answers to be the very expensive range. With a much more reasonable top end, you can get by with much less expensive coax since loss is generally
much higher as you get higher in frequency. For example, if your top frequency is actually in the 900 MHz range your good coax will be several dollars per foot less.
You'll need some very good coax to transfer signals from a unity gain antenna down 75' to your receiver at 3 GHz. At the minimum, some quality heliax like LDF4-50A (3 dB loss) or even LDF6-50A (1.3 dB loss) may be necessary. At a more reasonable 900 MHz top end, you can get by with some LMR-400 and still be under 3 dB of loss (at 900 MHz).
Find a good coax loss calculator (Google that phrase to find several) and plug in your values to find what will work good for you. Here are a few links to get you started:
Coax Calculator
Coax Loss Calculator
Should I amplify the signal?
Only if you need to. An amplifier will increase both the signal and the noise. A receiver needs to have the signal to be significantly above the noise to properly select it out for processing. If you amplify too much noise there won't be enough signal to pick out above that noise.
For example (not real numbers, but something to explain what I'm saying). Your receiver may need the signal to be 10% above the noise level for proper processing. You start out with a signal level of 100 units and a noise level of 90 units. You have the required 10% and can process the signal. It may be noisy, but you can do it.
You get an amplifier that boosts the signal to 200 units and the noise to 190 units. You still have 10 more units of signal to noise, but your ratio is now below that magic 10% level so your radio may not correctly process the signal.
Another issue is overload. Prior to amplification, some nearby strong signals may still be low enough so your receiver can properly ignore them. Once you amplify everything, they may be sufficiently strong to overload your receiver and you can no longer pick up much of anything.
Only if you have something in the line (like a preamp) that needs power and you don't want to run a separate power feed.
I am near transmission lines... Need a noise filter?
Are they noisy and interfere with your signal? If so, perhaps yes. If not, no filter is probably necessary.
