Thank you so much for your tips! It is much appreciated.
Yes, the club will be more of the form of friends watching and discussing the movie - we all know each other.
I think the double feature is a really good idea and having both films be about a general theme. I think I'm going to try that for the first night.
Thanks again!

Much depends on the nature of the club. Is it simply a group of friends who want to watch films of any genre/decade, or is there some focus? If its the former, then you may want to select (by vote or other mutually agreeable means) a theme for each monthly viewing and since its only once per month show a double feature. Themes could be as varied as screwball comedies with snappy dialogue, films that couldnt be made in modern Hollywood, mind-boggling sets and costumes, etc. Showing two films fitting the theme would give your group all sorts of conversation starters in terms of comparison and contrast.
If you dont want double features, you might compose a scorecard for members to mark as they watch. Depending on the film, you might keep track of double entendres, number of times a cowboy fires a six-shooter without reloading, glasses of wine/beer/booze poured or consumed, etc. Who knows you might make a game out of it, perhaps even a drinking game.
Of course, thats all frivolous stuff. For more serious discussion, you might suggest that individual members be on the lookout during the movie for different elements, such as overlapping dialogue, an unreliable narrator, mistaken identity, a message conveyed by expression rather than words, or other aspects technical or dramatic that are likely to be found in the movie youve selected. Or you could present a list to the group as a whole and let them spot the elements as they arrive (or note their absence). At the end, a likely starting point for discussion is the filmmakers use of each element and its purpose and/or effectiveness in the production.
I hope you find some of the above useful!
I've been ionized, but I'm okay now.