If I have to take off in a C152 or C172 from a runway that's 800-900 meters (2600-3000ft) long and wet but not contaminated, what flap setting should I use to get the shortest ground roll?
The POH for a 152 lists the flap settings for takeoff as between 0° and 10°. It makes no specific mention of take off from a wet runway, however you could follow the same procedures for a soft/rough runway if you are concerned about the surface conditions.
Soft or rough field take off are performed with 10° wing flaps by lifting the aircraft off the ground as soon as practical in a slightly tail low attitude. If no obstacles are ahead, the airplane should be leveled off immediately to accelerate to a higher climb speed
Source: Cessna 152 POH Section4 (Normal procedures)
I should note though that in roughly 180 hours on C150/152's and a short (650m) hard runway, I've never felt the need to even use flaps, let alone execute a soft/rough field takeoff as described above. It's not a particularly comfortable take off, and a wet hard-surface runway doesn't really present that much of a problem.
You don't give a lot of detail, e.g. altitude, temperature, obstacles. But the last time I flew a C172 there were no manufacturer operational restrictions for wet runway for this aircraft.
Bear in mind that a wet runway may nevertheless affect takeoff performance for various reasons e.g. harder to track aircraft, engine performance and so forth. But short answer is that flaps would be the same as for dry conditions, 10°.
Wet is such a varied expression. How much water are we talking about ? Just a little wet, some water puddles, or the whole runway has a few mm of water all the way through ?
Realize tires on such planes aren't that dissimilar to car tires. Can you drive at takeoff speeds without feeling the water is dragging the car ? If you can, you fly and take off the same. Try this out on a road near the airport (which received the same volume of precip and is just as flat as the runway).
I'd use first notch of flaps and would hold the aircraft until full power is achieved and then release so you don't waste any runway distance.
Doesn't matter if the runway is slippery. What matters is if the water produces significant extra tire drag that reduces acceleration. Probably obvious by might not be to others.
250 hours flying C150/152/172. Very few takeoff / landings on wet runways.
Look up the POH and make sure you have some extra runway length to spare just in case.