The laws of how Tefillin are made are extremely complex.  For every part of the Tefillin there are many different opinions in Jewish law about how they should be made.  Some are more stringent and others are more lenient. 

For example, there is a debate in Jewish law over whether the Tefillin box must be made out of one solid piece of leather or if it is sufficient to glue together several pieces thereby forming one piece.  The prevelant custom is to rely on the leninent opinion when neccesary.  But if one wants to fulfill the mitzvah of wearing Tefillin according to a higher standard they should choose Tefillin made from one piece.  

This is just one example of hundreds of rules where there are differences of opinion.  Generally our standard Kosher Tefillin are made according to the more lenient standard.  Our superior or deluxe Tefillin are made according to a more stringent standard for those who want to do the Mitzvah in the best way possible.

The general rule of thumb is that you should choose the best Tefillin that you can afford.

For the purposes of Tefillin we determine if you are right or left handed by which hand you use to write.  So if you write with your left hand, you would choose lefty Tefillin.

If you alternate hands, you need to consult with a competent Rabbi to help you determine which arm to put Tefillin on.