My aunt is a ceramic "art-tist" and does not use a potters wheel. You can easily make bowls and plates without the aid of a wheel. Make sure when drying that you either keep the clay in the mold or prop it up to prevent warping or cracking.
If you will be using the end product for food, you will need to make sure you have the proper clay which will need to be fired in a kiln, painted with NON LEADED food based paints and fired again. Only then will it be satisfactory for food.
If you are going to be making knick knacks then other clays would be fine. I have a thing of Crayola air dry clay which I like very much. I did have to leave my products out for a week before sufficiently dried.
If you're just starting out, try going to a paint it ceramic place. That way all the supplies are supplied as well as the kiln. Two schools I went to had kilns, so you can look into that too.
Here's what my aunt makes, sans wheel.