What do you see as the primary purpose of the club?  These are significantly different types of organizations and there are significant trade-offs in determining the tax structure.

You would use a (c)(3) charity if it is intended to be generally educational for the general public.  Members could claim charitable deductions for their membership dues to the extent that their dues provide general support for the club and don’t buy specific services such as a certain number of hours flying the club’s aircraft.  You would probably need a real educational purpose to qualify as a (c)(3) and would probably have to open the services to the general public beyond the members of the club.  With a (c)(3) you would be limited in the amount of lobbying you could undertake on flying-related legislation and could not support or oppose candidates for public office.

You could consider a 501(c)(4) social welfare organization if you are primarily concerned with lobbying and electioneering.  Contributions and dues would not be deductible for a (c)(4), however.

You would need to promote a line of business of your members if you want to qualify as a (c)(6) trade association.  You might promote commercial pilots, or charter airlines, but it doesn’t sound as though that is what you really want to do.  A (c)(6) would give you a greater right to lobby on legislation and would remove the prohibition on electioneering, but you have to qualify for the status before you get the benefits.  It doesn’t sound as though you would be promoting a line of business of your members.

It sounds like you might more appropriately be a (c)(7) social club, offering social and recreational activities, which could include educational discussions and flying opportunities for a group of congenial members.  To qualify as a social club, you need to be sure that you don’t exceed the limits on the percentage of your club’s income that may come from non-members.  A number of clubs have lost their exemption by offering rental facilities or educational lessons, like golf lessons or sky diving lessons, to non-members so that too great a portion of their income has come from non-members.  If your members are really concerned about deductibility of their dues, they should be aware that IRS says that dues to a social club generally cannot be deducted as a business expense (See IRS Publication 463), although some specific business-related meals or entertainment might be deductible.

I am sure there are other issues to be considered.  Your group should decide what your primary objectives are and how you can best achieve them within the limits of the various classifications.