after.html

{exp:query sql="
        SELECT     md.entry_id, cd.field_id_56, md.col_id_48
        FROM       exp_matrix_data AS md
        LEFT JOIN  exp_playa_relationships AS pr
        ON         md.entry_id = pr.parent_entry_id
        LEFT JOIN  exp_channel_data AS cd
        ON         pr.child_entry_id = cd.entry_id
        WHERE      md.field_id = 123
        AND        md.row_order = 1
        GROUP BY   md.entry_id
        ORDER BY   md.entry_id ASC"}
    {exp:stash:set name="phone_{entry_id}" cache="no"}{if col_id_48}{col_id_48}{if:else}{field_id_56}{/if}{/exp:stash:set}
{/exp:query}

<ul>
{exp:channel:entries  channel="channel_name" sort="asc" limit="250" disable="categories|category_fields|member_data|pagination"}
    <li>
        <div class="info">
            <p class="contactInfo">
                {exp:stash:get name="phone_{entry_id}" cache="no"}<br/>
                <a href="mailto:{emp_email}">{emp_email}</a>
            </p>
        </div>
    </li>
{/exp:channel:entries}
</ul>

before.html

<ul>
{exp:channel:entries channel="channel_name" sort="asc" limit="250" disable="categories|category_fields|member_data|pagination"}
    <li>
        <div class="info">
            <p class="contactInfo">
                {contact limit="1"}
                    {if direct_phone}
                        {direct_phone}
                    {if:else}
                        {office}
                            {office_phone}
                        {/office}
                    {/if}
                {/contact}<br/>
                <a href="mailto:{emp_email}">{emp_email}</a>
            </p>
        </div>
    </li>
{/exp:channel:entries}
</ul>

description.md

Channel Fields

contact is a matrix with 3 columns: office, direct_phone, direct_fax
direct_phone & direct_fax are text fields
office is a single select playa field
office_phone is a text input on the offices channel

SQL Explanation

SELECT     md.entry_id,                               # Get the {entry_id} from matrix_data,
           cd.field_id_56,                            # {office_phone} from channel_data and
           md.col_id_48                               # {direct_phone} from matrix_data
FROM       exp_matrix_data AS md                      # 
LEFT JOIN  exp_playa_relationships AS pr              # 
ON         md.entry_id = pr.parent_entry_id           # 
LEFT JOIN  exp_channel_data AS cd                     # 
ON         pr.child_entry_id = cd.entry_id            # 
WHERE      md.field_id = 123                          # where the matrix field is {office}
AND        md.row_order = 1                           # and only grab the first row.
GROUP BY   md.entry_id                                # This prevents extra columns from playa_relationships.
ORDER BY   md.entry_id ASC                            # Order by {entry_id}

Stash

I check if the person has a direct_phone and, if so, store it in Stash. If not, store the office_phone from the office they are in.

I am using cache="no" so the Stash vars aren't written to and read from the DB.

Conclusion

This method reduced the number of queries on this page from ~800 down to ~40 per (uncached) page load.

If I remember Low's Parse Order presentation well, modules {exp:tags} are parsed in the order they are in the template. If nested the parser deals with them from the root of the document inwards