Best PCB etching method

I don't know but there are companies that specialize in it. I'm pretty sure chemical etching is still the standard method.

There are ways for hobbyists to do it but most electronics companies farm it out and there companies that specialize in fabrication for hobbyists or prototyping.

I've had a couple boards made by Seed Studio/Fusion and I got 10 or 20 small boards for less than $100 total, including DHL shipping (before the current tariff situation). They are made in China. It took about 10-14 days. They were double-sided boards with silkscreen & solder mask, etc. More "professional" than I could have done myself.