I was researching what frequencies are usually used for coaxial Tx. Most sources just says that at low f the length of the line doesn't matter and vice versa. However, I couldn't find a source that indicates the best f are used for transmission lines to transfer power. So what are the best frequency range to use? khz, Ghz ?? And why?
No, the length of the coax (line) does matter in so far as loss goes.
For any type coax, there are two primary loss components, resistive and dielectric.
Resistive (or conductor) losses are a function of the conductor material (i.e. copper is a better conductor than aluminum), the frequency (which determines the skin depth of the current), and to a smaller extent, the roughness of the surface of the conductor. Resistive losses go up as a function of the square root of the frequency.
Dielectric losses are low for low frequencies and go up directly in relationship to frequency.
Both types of losses scale with the length of the coax. So doubling the length doubles the loss, assuming everything else stays constant.
At high frequencies GHz and above, coax is the preferred method for going between boxes, for instance, irrespective of the power involved. For really high power levels, coax breaks down because of the high E fields involved, and waveguides may be used (radar transmitters, for example).
The original Ethernet standard specifies 10 MHz. It's high enough for a decent data rate and low enough not to cause radio interference. If you look at the original standard document from a couple decades ago, it contains all electrical specs and circuits required so you won't need to develop your own. Plus you can buy stock connectors and cables.
It is meant for signals though, not power.