B.L.E.

The main thing about tail draggers is that the main wheels contact point is in front of the plane's center of mass while on tricycles, the main wheel's contact point is behind the plane's center of mass.
On trikes, the centrifugal force of a turn acting on the plane's center of mass, attempts to straighten the turn. The plane is not only nose heavy to the wing's center of lift but also nose heavy to the wheel's center of traction. This means that the plane is stable when rolling as well as when flying.
Taildraggers, are nose heavy to the wing's center of lift so are stable when flying but are tail heavy to the wheel's center of traction so they are unstable when rolling. The centrifugal force of a turn acting on the plane's center of mass behind the main wheels tries to tighten the turn and in extreme cases results in a "ground loop", a turn that goes completely out of control. During high speed taxiing, a taildragger may need some opposite control to kill a turn once it has started and you have to watch out for overcontrolling the plane. If you find the plane going into a series of overcontrol oscilalations, it's best to thottle back and abort the takeoff attempt.

Planes like the 4*60, ugly sticks, etc have enough tail area that aerodynamic stability is already dominating long before they are going fast enough to take off. That is, the rudder and not the tail wheel is steering the plane during the takeoff roll. Beginners need not fear these planes, they almost don't count as taildragger experience.

Soft foam wheels, because of their higher rolling resistance and lower grip, tend to reduce the positive feedback that make TDs unstable on the ground. Just like your car understeers and plows through turns when the front tires are underinflated, the foam wheels sideslip and don't tend to hook the plane into a tighter turn. Also, since the wheel on the outside of the turn gets loaded and the wheel inside of the turn gets lifted, the increased rolling resistance of the loaded wheel and reduced rolling resistance of the unloaded wheel tends to fight the turn and helps stabilize the plane on the ground. If you have ever flown in a full scale taildragger, you may have noticed the pilot using the individual wheel brakes to keep the plane straight as the plane slows down after a landing or during the early stages of the takeoff.

Like other posters have noted, there is no need to fear taildraggers, they aren't that hard to handle. If you pick a day when there is a little headwind on the runway for your first flight, you will have absolutely no problems. Taking off or landing downwind is just asking for a groundloop however.