I use pannier baskets on a full-size bike, open topped with just a hessian shopping bag in them to shield my stuff from envious eyes, but it must be said I live in a relatively crime-free area. The baskets I use are made by Basil, a Dutch firm which I've always found to make the best baskets and at a very reasonable price. The particular Basil basket I use is the Cardiff, which over the years has been fitted every I bought a new bike. My experience is that the Basil metal baskets are light enough (balancing durability and barrier capability in an incident with a badly driven Range Rover against weight), and the wicker baskets are heavier (I don't have a wicker basket but ladies among the pedal pals do). I mention Basil because they offer Klickfix on their more expensive gear. I've had Klickfix or Chinese copies on other gear like handlebar bags and found it perfectly satisfactory, though I rarely take e.g. the phone bag off the bike, just taking the phone out when I leave the bike.
If you buy a basket which fixes by a U-shaped rod on rack rails or handlebars or other bicycle tubes, you can both protect the bike's paint and plating and polish by wrapping a length of velcro, fixing to itself, around the tube where the Basil basket will fit, and stabilise and silence the basket with the velcro. It also makes it bloody difficult for a thief -- and the owner -- to take the Basil basket off, an effect I aggravate by applying a large visegrip gently to the rod. Crude but effective. When I have stuff to carry, I take out the hessian bag and use that.
The Basel Cardiff baskets I use have no bottom fixing because they're intended to be lifted off the bike and carried into the supermarket or the house by Dutch housewives, maximum daily convenience. I tie my semi-permanent installation to the bottom of the rack supports by a repurposed luminous Sam Brown belt with some bits cut of -- it goes around the basket and is seen from both the front and the rear by motorists, giving them an idea of how wide my bike is. When I don't need the visibility I use a military green canvas belt with rings for tightening it against itself; my bike is green.
After 30 plus years with them, need I say that I recommend Basil baskets? The ones on my daily bike, thirteen years old this coming December, are pretty tatty from winning arguments with cars and handy poles for leaning the bike against, so thank you for reminding me to get new ones.
Basil baskets:
https://www.basil.com/en/bicycle-baskets/ Here is the Cardiff I chose and have found such a good multipurpose carrier that I've across several bikes replaced it like for like, and intend to do the same on my daily bike:
https://www.basil.com/en/cardiff-basket-black.html 
Don't know whether or how it would work on a folder, but Basil also makes fold-flat baskets, some of them very large, so if you're interested in a basket that doesn't take a lot of space when not being a basket, you should check the weight of the folding baskets. I'm not a weight weenie, and I have a requirement for a hefty load (I think nothing of carrying a painter's solid wood rotary easel, guaranteed not to blow over just as I finish the painting) so I decided, rightly or wrongly, not to take a chance on the hinges of a folding basket being a week point when abused week in and week out by overloads: basically I concluded on no evidence back then that the lighter, fixed Cardiff would be stronger for longer and think I've been proved right.
Trivia: Old cyclists can remember when Basil's Cardiff pannier basket cost Euro 16.99, delivered, and a Bob Jackson custom-built road bike, fully fitted out with aspirational parts, left a lot of change out of a thousand pounds.
