Not-for-profit?
You have said that your organisation will have no members, will not be charitable, will not incorporate, and that the people in charge will get paid.
It sounds like your organisation may be more like a private business than a not-for-profit organisation. If you wish to be recognised as not-for-profit, you will need to change something.
You could reconsider whether to incorporate, and become a Community Interest Company (CIC). CICs are incorporated organisations that have an “asset lock” which guarantees that they will invest all their surplus income back into the community. This illustrates to the wider world that they are not-for-profit.
Your route so far:
Voting members? No. Charitable? No. Incorporated? No. Paid staff in charge? Yes.