If you want to be an independent personal trainer and have a client base to support you than thats fantastic!
There is no right or wrong way to build your business.
Find your niche, develop your business plan, market yourself, have proper credentials, do as much research as you can!
I personally managed a fitness studio for (ever) 25 years. I did my training there.
Today I have 2 outdoor bootcamps, an in home personal training business/health coaching business.