What kind and how expensive?

If you are talking about setting up a company that teaches firearms safety then you may wan to talk to someone in your state which already does that.  Like any other occupation the requirements will differ.  

Or check with the NRA.  As much as I am opposed to their leadership they do have a handle on what each state requires of THEIR instructors.  

I've been instructing for about ten years and below is what I learned talking with a couple lawyers and doing research.

Agree with the Liability Waiver if your state recognizes them. Waivers need an "In consideration clause", which basically means "if I provide XXXXX for you, you agree to XXXXX". They must also be written in a simple to read and understand format.

People will tell you to form a LLC as a means to shield yourself from liability... while it will shield you from SOMEONE ELSES negligence, such as a co-instructor working for you, an LLC doesn't automatically protect you from individual liability due to negligence.

Research individual liability insurance policies, you might be surprised at category limits. Although it was years ago when I checked, the instructor policy the NRA was selling, for about $350 a year, had a MEDICAL PAYMENT CAP of $5,000.00 despite the policy being advertised as a 1 Million Dollar Liability Policy. I found that misleading but that's what the guy told me. Maybe things have changed.

If you type in “firearms instructor insurance” and scroll down, you’ll see several options available.  Generally it’s offered by “outdoor” insurance groups, and you’re going to pay less than $500/year.  As has been pointed out, you need to have a solid liability waiver in-hand to give to your students.  Insurance companies will also require that.  Don’t just copy someone else’s waiver form, because I’ve seen that before and you have no idea whether it’s sufficiently protecting you.  Most insurance companies have restrictions on what they will and won’t cover, so be careful of what you do or allow.  They’re usually pretty common sense, but make sure they will cover you for what you want to do.  Case in point- some companies won’t allow the use of automatic weapons.  While this isn’t a big deal for most people, if you plan to offer firearms training to LE, you may need to restrict what firearms they can bring because many LE agencies- particularly SWAT teams- issue select-fire rifles  Point being, do your due diligence on choosing which company to use and make sure they have the coverages you want.  The training group I work with specifically has insurance that authorizes automatic weapons and scenario-based training because we do a lot of LE training.  

Some companies also have certain training guidelines where they want you to have some sort of qualification, so be aware of that one as well.  

Just food for thought.  Make sure that everything you want to do is going to be covered.  The more coverage you want/need, the more expensive it is.

I took a NRA RSO class thru MGO for free. The liability an instructor has, for even people not under his control is high.

I was just a RSO for MGO get together's, and didn't have insurance, so I let it lapse.

Lockton is pretty much the standard for NRA instructors:

https://locktonaffinityoutdoor.com/firearm-instructor-insurance/