You dont need extra supers for the bees to produce honey. They will produce where ever they are. I think you are asking do you need an additional super for the bees to make you some honey. It looks like that hive is 2 deep supers (hive bodies). The "normal" set up would be 2 deeps for the bees then additional medium or shallow supers for you. If you are starting with a package of bees this coming year you probably will be fine without buying the additional supers this year. but you never know I have had packages produce excess honey their first year.
If you have the money to buy extra equipment I would recommend buying a second hive to have on hand. You never know when you might run across a swarm or have the opportunity to split a hive. Nothing worse then coming across a obtainable swarm and not having equipment to put it in and having to let it go.
When you are just starting it is nice to have 2 hives with bees so you can compare the two. having 2 rather then one is really not that much more work, but it is double the fun
Welcome to beekeeping