How much thrust does a airplane need?

Depends on how powerful you want it to be.

Basically thrust has to be powerful enough to get the plane to take-off speed, or it'll stay on the ground. And then you'll want a bit more than that to get a decent climbing rate out of it.

Exactly how much it'll need in numbers is impossible to say, as it'll depend on the aircraft. A bigger aircraft will need more than a smaller aircraft. If you want high climbing rates you'll need more than if you're OK with low climbing rates.