Will a corporation or LLC protect me from liability?

One important aspect to keep in mind is that a corporation (or LLC) will not protect you from liabilities for your own actions! So, operating a personal training business through an LLC won't prevent you from being sued personally if you drop the weights on your client. There may be other advantages to doing so, depending on your circumstances, but liability protection for torts asserted against you isn't one of them.

But, suppose business is great and your hire a second personal trainer to handle a few clients. And that individual drops a weight on a client's foot and breaks it. The client can sue your company, and even the trainer that dropped the weight, but can't sue you personally. Of course, it's never that simple... a creative lawyer might allege that you failed to properly train or instruct the trainer, and it was that failure that caused him to drop the weight on the client's foot. But, absent those types of allegations or circumstances, your LLC has provided the liability protection you hoped it would.