You do not extend your green card validity by obtaining a re-entry permit. Though the card itself has an expiration date on it, your status does not expire when your card expires, though you should never let it expire without first applying for a new card.
The re-entry permit simply prevents CBP from determining that you have abandoned your residence solely based upon the time you have remained out of the US.
[8 CFR 223.3(d)(1) Reentry permit. A permanent resident or conditional permanent resident in possession of a valid reentry permit who is otherwise admissible shall not be deemed to have abandoned status based solely on the duration of an absence or absences while the permit is valid.]
The re-entry permit does not immunize you from challenge by CBP on your return that you have abandoned your legal permanent residence.
The simplest answer to your question about the anser on the form, is that your class of admission is "legal permanent resident."
You'd better get an attorney to advise you before you leave the US.