What is the best way to cut and paste clip from one track to another?

There are several good ways to do that actually. Here's one.

Start by ensuring you have the Event Inspector in your top section of your screen.

If you click on a clip or a track the Event Inspector displays the exact start time etc. of what you've clicked. You can then use Control X or Cut on the clip you've selected.

Then click on your target track. Use Control Alt V (paste Special).

Now you can type the exact start time you want because you can see it in the Event Inspector. It will with surgical precision put the clip at the same place but on the target track.

That's one way.

P.S. if you could use pointers and a brush up on the Event Inspector capabilities, Scott Garrigus did us all a favor with this video below:

http://www.youtube.com/watch?v=Ixb8gIcGM-U

Before I move a clip from one track to another, I like to make sure that the clip I am moving has a start time that is simple - for instance on the start of the measure, 1/2, 1/4, 1/8 maybe 1/16.  It is easy to make the clip wider at the beginning and use the snap option so it snaps at an interval.  Then after moving, I can trim the clip knowing that it is at least in the right place for the music.

I normally "nudge" the clip up or down using the 8 and 2 keys on the number keypad. This way  ensures that it retains its position on the timeline.

If the clip that you wish to move is in a take lane, select it first and then turn the take lanes off. The selected clip, when nudged, will always move to the next track rather than move between lanes.