NASM is routinely accepted by most clubs, but, understand, if you can make $10/ per 1/2 hour session, you'll be lucky, in any chain club, where you'll likely also be asked to push supplements (e.g. 24 Hour Fitness), it may not be a $30k a year job, at best.
NASM is not a good approach for training many folks. E.g., it's idiotic to have folks doing unbalanced exercise in many instances.
Cooper, and NCSA, are probably a couple of the most highly regarded.
You can work for a training studio, but, unless you manage to get a lot of consistent clients, at a good rate...you'll never really make a decent living.
If you want to make decent money in the training world...you really need to be at least a Master of PT, or, DPT. While you won't be stuck in retail sorts of wages, you'll still have issues getting to over 100k in most situations, even with a 4 year degree. A DPT, can start higher, and make 150K, or more, after a few years, but, probably won't get more than 75K when he first starts out.
Now, you could train folks for 20 years, and start your own studio, and have other trainers working for you, and line your pockets.
The trick is finding a place that pays a decent wage.
The vast majority of NASM trainers are idiots...even on a good day. The industry rather likes it that way, at least, in large scale enterprises.
You can also get a trainer's cert, and maybe work within a large enterprise wellness program, but, understand, the vast majority of the folks barely make enough to live on, much less plan for retirement.
You should expect early mornings, and well as evenings, if your clients are working class. More well to do folks go to studios, or have their own home gyms, and they expect you to make house calls (follow the money).