The first film to be previewed at the Great Neck Arts Center's upcoming Cinematheque Film Series will be the star-studded Miramax film The Mighty, on Thursday evening, Oct. 8. Starring Gena Rowlands, Sharon Stone, Kieran Culkin, Harry Dean Stanton, Gillian Anderson, and Meatloaf, this film is the first in the Arts Center's fall series, offering subscribers an advance look at some wonderful upcoming films.

The Mighty will have its world premiere in Los Angeles on Oct. 7, the night before the Great Neck preview. It will not be until two weeks later that the film will be available for viewing by the general public.

''Miramax executives were so impressed with the turnout at last spring's film series, that they wanted to solidify a relationship with the Arts Center as a place to preview independent movies,'' said an Arts Center spokesperson.

According to Arts Center Executive Director Regina Gil, last season's success, coupled with the ''upgraded, modernized, and elegant'' Clearview Squire Cinemas, ''convinced Miramax to go with this young organization, to put the weight of their prestige behind us.''

The evening will include a viewing of the film, along with discussion led by Garen Thomas, an editor from Scholastic Publications. Ms. Thomas worked with Rodman Philbrick, the author of Freak the Mighty, the book on which the film is based.

Each preview in this film series will have an educational, as well as an entertainment, component, Ms. Gil explained. ''There will always be a speaker to illuminate the issues related to the film, the production, and the content,'' she said.

The Nov. 12 evening in the series will preview the film Down in the Delta, written and directed by Maya Angelou.

Smoke Signals, which was previewed at the Arts Center last spring, has just recently been released to public theaters, and laudatory write-ups are appearing in major publications. The Arts Center's spring Cinematheque preview was the first- ever showing for this now-popular film.

Excited about last spring's great success, and brimming with enthusiasm for the fall film series, Ms. Gil states that, ''This film series enhances the Arts Center's mission, a mission to promote and support the arts in the community.''

She and film series coordinator Deanne Lipsius emphasized that the goal of this Cinematheque Film Series is to ''help put Great Neck on the map as a place to see new movies before they are available to the general public.''

Ms. Gil added that they hope to develop a reputation, to be known as ''the place for the arts on Long Island.''

Ms. Gil will appear on Shirley Romaine's cable television show Artscene on Long Island later this month, and she will bring a film clip from The Mighty.

The fall Cinematheque Film Series will be sold by subscription only. This ''take four'' subscription is $80 for the four-film series. Only 200 subscriptions can be sold, and the Arts Center expects to sell out way in advance. However, if there are no-shows any evening, tickets will be sold at the door.

The film series will be held on the four Thursday evenings---Oct. 8 and 22, and Nov. 5 and 12---at 7:30 p.m., at the new Clearview Squire Cinemas.

For a subscription, or for further information, call Deanne Lipsius at the Arts Center, at 829-2570.

Series tickets can be charged on major credit cards.

And popcorn and soda will be served, on the house, to all who attend.