Legal structure for your group
You have said that your organisation will not have members, will not be charitable, and will be incorporated.
A possible legal structure for you is:
Community Interest Company (CIC)
This is a type of limited company. It guarantees its not-for-profit status through an asset-lock, which commits the organisation to using all its surplus income for the benefit of the community. It is led by a board of directors. Although it technically has members, you can choose to have a very small number of members, and all the members can be directors. The directors can be paid or unpaid, but having paid directors can make it harder to access grant funding.
Your route so far:
Voting members? No. Charitable? No. Incorporated? Yes.