The ease with which a non compete is enforceable varies from state to state is highly dependant upon the language of the agreement and the circumstances. In addition, depending upon your position at your current employer, you may have fiduciary obligations. Finally, one must proceed very carefully when planning a new business, taking particular care not to do things on "company time." In short, I strongly urge you to seek the advice of a New York attorney before proceeding too far down this path. Nothing kills a new business quite like litigation.
Just to add to Mr. McLain's correct response, it is also important to remember that the client list you collected while employed at that firm is likely to be property of the employer so that you would not be allowed to leave with that list.. Contacting your former employer's customers might also be called a "tortious interference" with their contract. Much of the business litigation my firm is involved in revolves around these issues. We have represented both companies and former employees who have started up rival businesses. As Mr. McLain stated it can be a tricky area. I would be glad to discuss it with you in a free consultation. My offcie number is 212 517 3200.