If you don't have a written lease, you have a month to month arrangement. The Landlord Tenant Law in NJ will tell you how much notice is required to terminate the arrangement, but I suspect 60 days is probably enough. You can search for this and find out exactly what your options are.
Having the home vacant and staged can make a huge difference when you are listed. Tenants may require up to 24 hours notice before showings and complicate the process.
I'd encourage you to start searching for your listing agent early. Often a good one will be able to help with many phases of preparing your home for the market and save you time, money and mistakes.
Best of luck with your sale.