In my opinion, the more coop space the better. You can get by with less in the summer, but if you have cold, snowy winters, your birds will likely be indoors for several months. This can lead to behavioral issues as mentioned earlier.
If you choose to hatch out chicks, you’ll need more space. If you can find a used shed, as mentioned in other posts, you can make a pretty nice coop with plenty of space for not a lot of extra money.
What are your plans for the chicks you would hatch? Keep the females to replace as layers? What will you do with the older hens? How about the cockerels? Bachelor pad? Eat them? It can be hard to find new homes for them.
If you want to be a good neighbor and keep them on your property, I would strongly suggest a covered, fenced in area.