I’m a bit of a veteran at this. All furniture with a stain or varnish reacts differently, often within the same piece let alone within a set. If you’re going to paint it, sand down any loose or damaged bits so they’re smooth. Then invest in a good quality stain blocker (look at the Zinsser range) or an all purpose primer which blocks stains. Apply as the manufacturer recommends. This’ll give you a good base for the paint. Then paint whatever colour you want with good quality exterior paint (you may need two coats). I don’t usually need a separate undercoat. Despite what I’ve seen on YouTube, read and tried myself, do not use a chalk paint (waxed or other finish). It’s too soft. Good luck. Just a couple of examples below.

I havent managed to paint the chairs yet but have hidden the yellow one from sight for now. I couldnt bare to see it there any longer ;-) (Sorry ED) I will paint them same colour as table the next time I have a spare moment. I've added a splash of colour to my vase... and I think that might be a safer option!!

If you have already completed the construction phase of the house, it will be a little more difficult to fit everything in. Thinking about the landscape design immediately when creating the project house is desirable. But if that wasn't possible, it's worth doing it now. Also, if you want to create a special interior in your recreation area, think through the color palette and style. Which will be in harmony with everything around. You can see everything you need to do this here https://www.gardenfurniture.co.uk. I think that if you add more bright furniture, it will look more lush and beautiful against the green garden. Shades of orange or blue would work for you.

I think it depends what the rope is made of. If it’s real cotton or flax I don’t think it would fare well, but if it’s plastic to look like rope (rather like faux wicker) then it may have a longer life. I’d love to see a pic as I’ve never heard of rope furniture!