Hi and welcome to TFP. The 4ft wide area is good for walking around the pool so it depends what you want as you near the house. I think if you want it weed free is to lay down weed cover and put river or bull rocks over it. Put it all the way to the house or leave a gap if you plan to plant flowers or bushes nearer the house. This may be easiest as I see it has a slope.
Alternatively, you can lay pavers if you want to expand the walking area. This will take more time because of the slope and ensure they are flat so no one trips. There is all types at Home Depot/Lowe's and you can do it a bit at a time as $$ are available. I would definitely put some weed cover on it now to reduce weeds and also any mush if it rains.
There is one last option - put ground cover such as monkey grass, mulch, Asian jasmine, pine needles, etc. This is probably the easiest and least expensive. All of these are low maintenance and keeps weeds under control.