We use the word paved, differently. I call the finish material of any surface prepared for walking or driving, paving. In other words, cinders could be a type of paving. they're just not asphalt or hard. They're "soft" paving. I guess that weed paper doesn't really work then ...? Figures. It depends on what part of the country you're in as far as what's available for paving (granular material-wise) but shopping locally resolves the question. Just don't get anything that is loose and doesn't pack. It must pack in order to be "walkable." (To pack it must include material sizes from fine to coarse grit ... but probably nothing larger than 3/4".) Granular material (cinders, stones or whatever) will NOT stop weeds. It is only diligence that will bring weeds under control. The trouble with fabrics and papers is that soil accumulates on top and weeds start. Then their roots penetrate the barrier. The "fabric" itself is sometimes very difficult or impossible to remove. I consider it a total waste of effort except for certain fabrics for certain possible OTHER uses. I've used cardboard covered with mulch for pretty good results, but this solution is temporary, too. Some weeds can still penetrate the cardboard from below and eventually many will sprout from above. If you can't use chemical control, then you must resort to other methods (light starvation and hoeing, etc) that you can keep up with. Keeping ground free of weeds is kind of like raising a child. If you let kids get away with anything, they will forever continue. If you let them know it's not even possible, they give up and comply. If you allow any weeds to persist, there will be a never ending crop of them. If you commit to constant weed eradication and normal mulching for 2 years (only the first year is really bad) then they will dissipate to almost nothing. In commerce, chemical control is the standard as otherwise, weed control would be prohibitively expensive. In most cases that means Round-Up. However, even that's not a panacea.

I'd put some structure in the play area, defining some lawn and having some garden beds. Yards always look really planned if you put in a strong shape, like the oval, here. I'd have grass, not gravel and no fountain. I'd make the grass circle fill most of the rectangle labeled "back garden," rather than have a path to a feature. This kind of structure makes a boring garden or a kind of random 'I love this plant and that one was on sale at the garden center' type garden look planned and elegant. Grass is better for kids to play on. However, if your grass struggles to grow and you risk having your lawn turn into a mud or dirt patch, then rethink. You want climbing plants, not a living wall. Plants grow, you if you have a wall full of healthy plants, they will grow and crowd out neighbors. And if you don't have healthy plants, your living wall won't look good, either. With kids and a narrow lot, you want to make sure your plants aren't full of thorns. I don't remember if Bougainvillea is or isn't. Trumpet Creeper is an option. You might consider putting a swing along the left wall of the back garden. If you put in something fairly elegant, it will be a feature to see from the patio and a place for adults to sit as well as something your kids will like. Or a hammock.

We did stamped concrete and brought it up right to poolside. So, no typical "coping" per se. Just the concrete rim around the pool. This photo is stamped concrete. This one is more of a bullnose edge. We did a square edge. You can still select a beautiful tile rim just below the edge. We also edged the steps with the small version of the pool tile.

Buy bigger pavers, 2' x 2'. Lay out a patio area for sitting and BBQ, then paths with closely spaced pavers for comfortable walking on each side leading you through the space. Plant drought tolerant California kind plants in the remaining space right in the gravel.