Tanning salons just underwent a large amount of bad publicity regarding skin cancer, etc. Therefore, I do not think this is the best current business idea.
Search the sites of www.tantoday.com and www.tantalk.com. I think it will be an eye opener for you. I have seen posters state that you need around $200,000.00 to open a salon. Depending on how big you want, it will not be that much. Leasing the equipment is an option. I know someone who said she would never go that route again. She paid about 3 times the cost of the beds in only 3 years. I would not recommend getting that deep in debt at 17. I do not think it is even legal for someone under 18 to sign a contract in some states.
grants are usually for non profit organizationsthere are SBA loans but unless it is something like $1000000, there are not many small loans out therea tanning salon has a lot of liability and unless you have lots of money and plenty of liability insurance, not a good idea