You can get a 501(c)(3) with an LLC however, you will have to declare yourself as a corporation when you file your taxes.

I'm not exactly clear why you think you need a business plan to get a 501(c)(3) though... to even be eligible for a 501(c)(3) you have to have some non-profit purpose... and if you're going to go for a 501(c)(3) I would recommend you consult an attorney because while you may think this is the best option for you, it may not be.

Regarding your business plan, you may want to consider going and talking with someone at a SCORE office. They can sit down with you and talk you through the essentials.

Good luck!