Advice on key design

I have 2 tables, a parent (tbl_persons) and a child
(tbl_languages_per_person) as follows (a language table is also involved):

------------------
tbl_persons
------------------
* per_id
* per_name
* per_address

--------------------------------------
tbl_languages_per_person
--------------------------------------
* lpp_person_id
* lpp_language_id
* lpp_id

As you can see, there is an obvious key in the child table which is
"lpp_person_id + lpp_language_id", but I also need the field "lpp_id" as a
unique key which is a field that contains a consecutive number of type
serial.

My question is: what should I configure as the primary key, "lpp_person_id
+ lpp_language_id" or "lpp_id"?
Is the role of a primary key different from that of a unique index?

With respect,
Jorge Maldonado