Ok so you have 2 options here if you want to "move around the object".
1. Use gluLookAt() to change the camera position and move it around the object. If the ojbect is centered in the middle of your virtual window you can use something like this:
/* Spherical coordinates to cartesians.. Google for the formula
Note that you might have to switch some of the coordinates depending if your up vector is Y or Z
*/
eyeX = distance * cos(theta) * sin(phi);
eyeY = distance * sin(theta) * sin(phi);
eyeZ = distance * cos(phi);
objX = 0;
objY = 0;
objZ = 0;
gluLookAt(eyeX, eyeY, eyeZ, objX, objY, objZ, 0, 1, 0)
With this solution you need to change the angle theta and phi when you move the mouse and you can add keyboard shortcuts to change the distance value that will act as a zoom. Note that you don't need any glTranslate or glRotate if you use this technique.
2. Use only glTranslate and glRotate to rotate the object and move around it while not moving the camera. You won't need gluLookAt here. The equivalent of the code I posted above using glRotate and glTranslate would look something like this but note that it also depends on what you use up vector and on which plane you drew the object (most tutorials / people use XZ, I prefer XY and Z as up vector)
glTranslatef(0, 0, -distance);
glRotatef(phi, -1, 0, 0);
glRotatef(theta, 0, 0, -1);
glRotatef(90, 0 , 0 , -1);