Should I land a Cessna 172 with or without a little power?
This is really a question for your instructor: if you've been taught both methods then he should be able to explain when to use a little power and when not to.

Having said that, it all depends: there are good reasons to land with and without power, depending on the situation.

A normal landing with full flaps in a 172 is typically done without power. The Cessna 172S POH I have doesn't even mention power in the normal landing procedures; it gives a target airspeed instead.

A short-field landing is also usually without power, to minimize the runway distance needed. The same POH says:


  Power -- REDUCE to idle after clearing obstacle


For a soft-field landing on the other hand, it's normal to carry a little power in order to touch down as gently as possible and avoid sinking into the runway surface. The FAA's Airplane Flying Handbook says in Chapter 8:


  Power is used throughout the [soft-field] level-off and touchdown to ensure
  touchdown at the slowest possible airspeed,


Finally, you might also use a little power if you bounce on landing, to stabilize the aircraft and re-flare (runway length permitting). But that's a bit more challenging and most low-time pilots should just apply full power and go around instead.