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I’m really confused about which one of these flaps is used on take off and land?
I didn’t even know there were different types, I thought that the top configuration was the only used one today?
Also, which flap would a big airliner (like A320 use please)?
Jet airliners almost exclusively use slotted Fowler flaps as trailing-edge high lift devices, most of them single- or double-slotted, some even triple-slotted.
For takeoff, these are only partially extended to minimize drag (see also How do flaps help an aircraft take off at a lower speed, yet cause drag at the same time?). E.g. on the Airbus A320, config 1+F and config 2 are valid takeoff configurations, and config 3 and FULL are used for landing (see here for details: A320 flap settings).
Some airliners are certified for a flaps up takeoff (e.g. Airbus A300 and A310), but this is pretty rare and requires very high takeoff speeds.
Airliners also have high lift devices on the leading edge of the wing. Most use slats, some also use Krueger Flaps.
There seems to be a misconception in the question. Different aircraft have different flap systems, which are those depicted. But it's not like an aircraft has all those types of flaps and chooses some of them for different things.
There is usually one system of flaps (in airliners two, really, between flaps and slats) that is used for everything. Different maneuvers require different settings.
I’m really confused about which one of these flaps is used
Before answering that question we have to understand why there are so many kind of flaps. The main difference among the flaps in your picture is their complexity and efficiency.
Regarding complexity, just compare the actuating mechanisms of a simple plain flap in respect to a double-slotted flap:
(Plain flap, source)
(Double-slotted flap, source)
A plain flap just need a couple of hinges to work, while a double-slotted flaps need several linkages, actuators and tracks to move. Complexity obviously implies also an higher price and more maintenance.
Regarding efficiency, said "$∆C_l$" the gain in lift coefficient that the flap needs to supply, an efficient flap generate less drag than an inefficient one:
(Polar comparison for different kinds of flaps, source)
Looking at the plot on the right, just say that for our approaching manoeuvre we need a $C_l$ of 2: following the plot we see that a plain flap generates a relevant drag coefficient of 0.1 while a slotted flap generates only 0.05 i.e. half of it. Looking instead at the plot on the left, you can see that a plain flap reach that $C_l$ of 2 at some 15° angle of attack, dangerously close to the stall region; a slotted flap reaches the same lift coefficient at some 5° with a good margin to stall.
Summarising, going from top to bottom, we encounter flaps with growing complexity but better efficiency: a plain flap is easy to manufacture, maintain and actuate than a double (or even triple) slotted flap. Anyway the latter is more efficient and possibly safer.
which flap would a big airliner (like A320 use please)?
Typically you'll find a plain flap on GA airplanes and a double-slotted flap on a jetliner.
The type of flap “used for landing” will depend on the aircraft being flown. Basically you will use whichever type of flap is installed on the airplane.
You don’t have a choice inflight, airplanes are designed and built with a certain type of flap depending on their size and complexity as other excellent answers point out.
There’s just one flap handle with different positions, and you will likely use different settings for takeoff and landing, but that’s about the only choice you have.
