First question: Can you afford $30,000+ and the two years it will take, plus wait time for acceptance, plus qualify for, a traditional resident gunsmith school? If so, there are about six to choose from, all with wait times and admission procedures to go through.
If not, you have a choice of online/correspondence schools. If you need a college degree, the only one you have as an option is Sonoran Desert Institute. If the degree is not required, American Gunsmithing Institute and Modern Gun School are alternatives.
AGI has a better teaching technique and great support, SDI uses a lot of YouTube personalities and teaches at a lower overall knowledge level and Modern Gun School has specific tasks they teach, along with projects you must turn in.
You will see many posts on the internet about how people will never go to a gunsmith with online training, how you must have machinist's training, how online training doesn't qualify as training and how you can never get a license to work from home. All of those are false. You'll also hear how you can't earn a living as a gunsmith, how you're going to get raided by the feds and how you'll have to pay more in fees and taxes than it's worth. All of these are mostly false.
There are over 50,000 working gunsmiths in the US now, a number that hasn't changed that much over the last few decades. If there is no way to earn a living at it, that number would be going down. There are about 25,000-30,000 FFL holders working from their homes. Puts that "You can't get a home FFL" argument to rest. Many gunsmiths don't own or use a lathe or mill. Since gunsmith schools graduate about 100-150 students a year, there are a ton of working gunsmiths who never went to one.
As for a living, you won't make as much as an airline pilot, software engineer or CPA. But you can make a living wage, doing what you want, where you want to do it. You may get raided by the feds, but you have to be doing something wrong to have that happen. If you're buying 10,000 AR rifles a year and your records show 120 sales each year, you're going to get raided. As for fees and taxes, they are part of every small business. If you don't want to deal with those, go to work for someone else.
Now, your question is about the best way to achieve your goals. Sadly, nobody here can give you an accurate answer. The best way is individual, and your best way may be different from mine or the guy down the street's. Do your research, study your options and choose what you find to be best for you.
Good luck.
Jeff