>>1Although you appear to have written this facetiously, I've been thinking seriously about it for some time. We can do a lot for each other if we organize ourselves, and as you say, with all due deference to the freemasons, if normal people can do this, then it shouldn't be hard for us at all.
I suggest a short list of objectives, in order of importance:
1. Freedom to pursue the arcane arts, embodied in our case in programming, but including science, engineering, pure mathematics, and whatever else interests us
2. Survival of the society
3. Acquisition of arcane power
Although tolerating, say, Java would be a choice I would oppose, I don't think we should limit ourselves by formally rejecting certain languages or principles, or by tying ourselves to ones that are at some point desirable. This practice extends to social issues as well, in that we ought to be above the drudgery of politics. We can best deal with the control-freak bogeymen - personified most forcefully at the moment by SJWs and the NSA - by ignoring and excluding individuals who are more active in the social and political arenas than in those of direct interest to us. While it would not be proper to prevent members from taking a political stance, a political or social cause is not something the organization as a whole should endorse.
I also have a suggestion regarding leadership which I think aids the survival of a society composed of intelligent people. Our activies as an organization will focus largely on the completion of projects, whether they are software or pure research. Project selection can be accomplished by a leaderless organization, in which individual members are free to choose to participate on a project or not as they like. Most likely, some people will always work on their own, while others will usually collaborate. Within the scope of a project, the individual or group responsible for its inception would run the show. This would
A. maximize freedom
B. maximize enjoyment
C. permit collaboration on large projects without affecting A or B
D. limit the influence of new, more naive members, while offering them a wide range of options
and probably other things, I don't know. Valve has done something like this, and the danger has been shown to be the formation of cliques. This is inevitable, but should and can be discouraged, since it is an ape-habit, and not the business of our hypothetical society.
Selecting new members could be accomplished in a manner like the one the freemasons use: invitation of individuals by one or two of our own, followed by some kind of evaluation by other existing members. I hope it goes without saying that non-practitioners - salespeople, laborers, and so on - will be excluded from membership, and should ideally not know the nature of the organization they are serving.
This leads to economic concerns. In order to effectively accomplish goal 1 (freedom to pursue study) without endangering goal 2 (our survival), we must derive profit from some fraction of our projects. However in accepting the limitations of commerce, we limit the degree to which we can fulfill goal 1. I see two ways around this. One is obviously to find projects which are both enjoyable and potentially profitable. The other, which is possible only in a mature organization, is to require initiates to serve a short time in projects not of their choosing. In this manner they would be treated as apprentices, and could additionally evaluated for full membership.
The point of founding this sort of society would be to free us from working on projects which are beneath us while furthering projects which we do value, a goal which is very much in our interests. It is not reasonable to expect that the ideas I have laid out here are perfect, but I hope they form a starting point from which we can build, as OP put it, a secret society; some kind of mages' guild.