Rather then moving one clip over the other I suggest you try putting the clips right next to eachother and pick a transition from the transition room. You have more control over the way the transition between clips happens. You can also selected between overlap and cross (this is also a setting in the preferecnes). I suggest that you experiment with these and see what suits you best.
Notice that you can drag the transition from the room into the timeline, and that the positioning of the transition is important: place it at the end of clip one or the beginning of clip two or overlap between 1 en 2. Also experiment with that and see what happens and suits you best.

Given the plethora of transitions available and the way professional film makers apply transions (have a look at what happens in movies and on TV), you will gradually find out that the best thing might be to not use any transition at all (just a hard change between clips), or a simple fade. All the other stuff may be used for exceptional situations in exceptional movies.

Have fun!