For insurance, I and a number of other school owners I use go to West Point Insurance. www.westpointinsurance.com
. The reason we use them is that we teach weapons and higher contact curriculums - MMA, Krav Maga, etc. They cover everything. The thing you'll find is that insurance is very expensive to get started, and they want the premium up-front in a lump sum for this type of thing. In 2.5 years, I haven't had a claim, with about 250 active members.
If the facility you are renting doesn't ask to see a certificate of insurance, you might want to start with forming your own LLC corporation or "S" Corp and getting insurance after you are cash flow positive. Forming a corporation will keep you from being personally liable in many instances. I'm not giving you legal advice, but if you want to shell out $1000 or more before you even get started, this is what you are looking at.
For mats, rolling them up and putting them down is going to be a problem, if you do it every time before you train. Plus, they might move around on a floor that isn't carpeted. Swain Dollamur mats roll out, and I use them in my front training room. (I have them down permanently)
All of the good mats are expensive, but last a long time if you take care of them. (Swain - both the old-style 1X2 meter and dollamur, and Zebra) The 1X2 meter mats just aren't tenable for moving in and out. Consider starting without mats, or having a mat just for working on throws or takedowns, if you do them. Check eBay, as there is always an MMA school that is closing and selling equipment. I've gotten all of my mats used. Zebra also has close-outs on mats that were used just once for grappling competitions.
12-16 year olds is a tough market. 90%+ of my marketing for kids is geared for 5-12 year olds. Just over 50% of my members are adults, so I'm not a "kids" place only. I train 12-13 year olds with the kids, and 14-16 with adults. If you are not training the kids in gi's you're really going to have to educate your buyer - MOM. Moms understand the personal development taught by martial arts when we show her, but most don't want their kids training at an MMA or RBSD place. Once kids hit 12, they are generally locked into "their" activities. I have maybe 8 13-16 year olds out of 250. I do this for a living, and I think I'd starve if I focused on this demographic, just as I struggled spending too much time on competitive MMA - 18-24 year olds with no money, no ability to meet reasonable commitments, just looking forward to next fight/weekend, etc. I do better with 3-4 year olds than either of these other age groups.
I can forward you some standard language for a waiver, if you message me with your e-mail. I'd highly recommend doing a MA Business Bootcamp through someone like Premier to open your eyes a bit. The martial arts part has been easy for me (Except teaching average 25 classes per week), the business part has been hard. You can do these camps for a flat fee, keeping in mind that people will want you to sign up for consulting, licensing, etc.
Most importantly - Good Luck...try not to lose the love for what you do when you start having to spend more time on the business side of things.