Pilots of nosewheel aircraft-that is to say, every type of trainer that you most likely will fly-are taught to bring the nose up to a full-stall attitude that allows the main gear to touch down (gently), followed by the nosewheel. (There's more to the landing than that, of course, but we're speaking in general terms.)
With tailwheel aircraft, or taildraggers, the objective is also to land straight and stay coordinated, but there are two ways to touch down. A taildragger wears the main landing gear up front but has a smaller wheel positioned beneath the tail. (Think Piper Cub, Luscombe, or the newer Citabria.) You could try putting that tiny tailwheel down first, but it would be tough on the wheel.
The preferred methods are the three-point landing and the wheel landing. In the first, the pilot plants the airplane (gently) on all three wheels at once after pulling back on the stick to bring the airplane to a full-stall attitude. It results in a slower approach that's ideal for uneven surfaces, because it keeps the propeller blades well clear of terrain, pebbles, and the like. In a wheel landing, the pilot eases down onto the mains while maintaining forward pressure on the stick during the rollout-the aim is to let the tail come down on its own as you decelerate. This provides a better view down the runway and can be useful for strong crosswinds, since it gives the pilot greater positive control of the aircraft (the aerodynamic surfaces are still providing lift). It eats up more runway on the rollout, however.
Both landing styles require a lot of rudder inputs and coordination to keep the airplane going straight in the direction of travel before, during, and after the rollout.