What type of DC motor do you need to change direction of rotation by simply switching polarity?
You can reverse the direction of rotation on any DC motor. Some of them require that you physically reconnect their windings, and that may require disassembling the motor first.
Here are the most common DC motor designs:
Shunt wound
Stabilized shunt wound
Series wound
Compound wound
Of those, the shunt wound is the simplest to reverse - swap the polarity of the power connected either to the field or to the armature. The other three designs require physical reconnection of the armature and field windings to reverse. "Brushless" DC motors are AC permanent-magnet synchronous motors.
You can use induction motor and can change the direction of rotation by changing two phase of its power supply. It will also be cheaper to use induction motor.
If you want to drive the motor with just DC voltage and no special switching drivers required, you need a brushed DC motor (with permanent magnets). Examples of such motors can be found in most cheap motorised toys, where to change the direction of spinning, you change only the polarity of applied DC voltage.
If you need speed and power though, I would recommend looking at brushless DC motors, but know that they need a driving circuit to work at all.
