The first think to address is your database engine, MyISAM. The database engine is how MySQL stores the data. For more information regarding MyISAM you can view: http://dev.mysql.com/doc/refman/5.0/en/myisam-storage-engine.html. If you want to have referential integrity (which is recommended), you want your database engine to be InnoDB (http://dev.mysql.com/doc/refman/5.0/en/innodb-storage-engine.html). InnoDB allows you to create foreign keys and enforce that foreign key relationship (I found out the hard way the MyISAM does not). MyISAM is the default engine for MySQL databases. If you are using phpMyAdmin (which is a highly recommended tool for MySQL and PHP development), you can easily change the engine type of the database (See: http://www.electrictoolbox.com/mysql-change-table-storage-engine/).
With that said, searches or queries can be done in both MyISAM and InnoDB database engines. You can also index the columns to make search queries (SELECT statements) faster, but the trade off will be that INSERT statements will take longer. If you database is not huge (i.e. millions of records), you shouldn't see a noticeable difference though.
In terms of your design, there are several things to address. The first thing to understand is an entity relationship diagram or an ERD. This is a diagram of your tables and their corresponding relationships.
There are several types of relationships that can exist: a one-to-one relationship, a one-to-many relationship, a many-to-many relationship, and a hierarchical or recursive relationship . A many-to-many relationship is the most complicated and cannot be produced directly within the database and must be resolved with an intermittent table (I will explain further with an example).
A one-to-one relationship is straightforward. An example of this is if you have an employee table with a list of all employees and a salary table with a list of all salaries. One employee can only have one salary and one salary can only belong to one employee.
With that being said, another element to add to the mix is cardinality. Cardinality refers to whether or not the relationship may exist or must exist. In the previous example of an employee, there has to be a relationship between the salary and the employee (or else the employee may not be paid). This the relationship is read as, an employee must have one and only one salary and a salary may or may not have one and only one employee (as a salary can exist without belonging to an employee).
The phrases "one and only one" refers to it being a one-to-one relationship. The phrases "must" and "may or may not" referring to a relationship requiring to exist or not being required. This translates into the design as my foreign key of salary id in the employee table cannot be null and in the salary table there is no foreign key referencing the employee.
EMPLOYEE
id PRIMARY KEY
name VARCHAR(100)
salary_id NOT NULL UNIQUE
SALARY
id PRIMARY KEY
amount INTEGER NOT NULL
The one-to-many relationship is defined as the potential of having more than one. For example, relating to your portfolio, a client may have one or more projects. Thus the foreign key field in the projects table client_id cannot be unique as it may be repeated.
The many-to-many relationship is defined where more than one can both ways. For example, as you have correctly shown, projects may have one or more tags and tags may assigned to one or more projects. Thus, you need the PROJECT_TAGS table to resolve that many-to-many.
In regards to addressing your question directly, you will want to create a separate media type table and if any potential exists whatsoever where a project is can be associated to multiple types, you would want to have an intermittent table and could add a field to the project_media_type table called primary_type which would allow you to distinguish the project type as primarily that media type although it could fall under other categories if you were to filter by category.
This brings me to recursive relationships. Because you have the potential to have a recursive relationship or media_types you will want to add a field called parent_id. You would add a foreign key index to parent_id referencing the id of the media_type table. It must allow nulls as all of your top level parent media_types will have a null value for parent_id. Thus to select all parent media_types you could use:
SELECT * FROM media_type WHERE parent_id IS NULL
Then, to get the children you loop through each of the parents and could use the following query:
SELECT * FROM media_type WHERE parent_id = {$media_type_row->id}
This would need to be in a recursive function so you loop until there are no more children. An example of this using PHP related to hierarchical categories can be viewed at recursive function category database.
I hope this helps and know it's a lot but essentially, I tried to highlight a whole semester of database design and modeling. If you need any more information, I can attach an example ERD as well.