You've likely created a pool of persona candidates during your persona pattern [need to create a page for this and link] exercise.  The next step is to determine which persona will be the primary target of your design.  It is common to have a primary and secondary persona.

Primary Persona

"The goal is to find a single persona from the set whose needs and goals can be completely and happily satisfied by a single interface without disenfranchising any of the other personas", About Face 2.0, Cooper, pg. 71.  This persona is typically referred to as the primary persona.  By definition, each primary persona requires their own user interface in a particular application. You know you have more than one primary persona when their needs cannot be met by the same interface.  The fewer the number of primary personas the better.  If you have more than 1 for a small project and more than 2 or 3 for a larger project, you may want to check-in about the scope of the project.  The goal of using personas in the first place is keep us from designing for everyone (the system tries to do too much so does nothing well), which means we'll meet no ones needs.

Secondary Personas

It is also common to have a secondary persona.  The secondary persona's goals and needs can mostly be met by focusing on the primary persona. However, there are a few needs specific to them that are not a priority for the primary persona.  There may be small additions to the interface necessary to meet the needs of a secondary persona, but these additions should not negatively affect the experience of the primary persona.

Choosing Primary & Secondary Personas

After you have identified your pool of personas, you need decide who the product design will focus on.  The activity of choosing primary and secondary personas can be challenging.  After all, everyone is important.  Many of us have found a persona mapping activity useful in forcing us to choose the most important personas and their priority.  This activity was originally introduced to a Fluid designer through Menlo Innovations HTA practice. 

The basic premise is to use a bullseye and small movable representations of your personas to spur discussion and a decision about who goes in the bullseye (primrary), who goes in the secondary ring and who is on the outside (tertiary or some of the "other persona types" describe below).  This is meant to be a very interactive activity.  All participants should be standing and moving persona cards around during the discussion.  Including project stakeholders in the activity can be a great way to gain their buy in.

To create this map the designers drew the circles on a large sheet of easel paper and used index sized cards for each persona.  The cards for the actual activity included a picture along with a brief bulleted list of description and goals. 

Other Persona Categories

Alan Cooper, who introduced Personas in "The Inmate Are Running the Asylum", defines a few more categories of personas in About Face 2.0 (pg. 72):

• Supplemental Personas - needs are completely satisfied by one of the primary interfaces yet they are part of the set or personas to ensure comprehensive representation.  They will not be a focus during design but let the entire project team know they haven't been missed by simply being represented.
• Customer Personas -  are not the end user but the customer of the product, perhaps the person making buying decisions.  You may need to take their needs into consideration for obvious reasons but just as with the secondary personas, you do not want their needs to get in the way of the primary persona fullfilling their needs.
• Served Personas - do not directly use the product you are designing but they are somehow affected by the system.  As a customer in a grocery store, you are not a user of the register (unless it's self-check) but you are served by the register having an efficient, easy to use interface.
• Negative Personas - are used to remind you and communicate with the rest of the team, who is NOT the target of the design.  A good example of a negative persona is a tech savvy, early adopter type person for a consumer product. 

Provisional Personas

A provisional persona is a persona created using historical, anecdotal, or statistical knowledge about a certain type of user, but is not based directly on patterns seen in user research. Provisional personas can be a helpful tool for capturing the team's knowledge about users when talking to actual end users isn't possible. However, they should be used with caution as they may not be entirely accurate or representative of the user population. When creating personas, we recommend performing some type of research with actual end users whenever possible.

Any of the persona categories above can be represented as a provisional persona.