There are different schools of thought on this. One school prefers including a primary key and naming the linking table something more significant than just the two tables it is linking. The reasoning is that although the table may start out seeming like just a linking table, it may become its own table with significant data.
An example is a many-to-many between magazines and subscribers. Really that link is a subscription with its own attributes, like expiration date, payment status, etc.
However, I think sometimes a linking table is just a linking table. The many to many relationship with categories is a good example of this.
So in this case, a separate one field primary key is not necessary. You could have a auto-assign key, which wouldn't hurt anything, and would make deleting specific records easier. It might be good as a general practice, so if the table later develops into a significant table with its own significant data (as subscriptions) it will already have an auto-assign primary key.
You can put a unique index on the two fields to avoid duplicates. This will even prevent duplicates if you have a separate auto-assign key. You could use both fields as your primary key (which is also a unique index).
So, the one school of thought can stick with integer auto-assign primary keys, and avoids compound primary keys. This is not the only way to do it, and maybe not the best, but it won't lead you wrong, into a problem where you really regret it.
But, for something like what you are doing, you will probably be fine with just the two fields. I'd still recommend either making the two fields a compound primary key, or at least putting a unique index on the two fields.