NB: I'm using the word 'community' in lieu of the word 'church' or congregation.
I know what I used to believe about organisational leadership in a community of Christians. 1 Timothy Ch.3 was firmly fixed in my mind. But that letter, attributed to Paul, is thought to have been written in the mid 60s CE. By that time some 30 years had elapsed since the death of Jesus and the formation of the first Christian community in Jerusalem.
Jesus left no clear instructions (known to us) for the organisation of a community of Christians. So we can only try to watch as the first community coalesces.
The book of Acts is not an historical document in a modern sense, but it paints a picture of what the author considered important in that first Christian community. In Acts ch. 1, we're told that 'about' 120 people were associating. These associates included Jesus own family, (his mother and brothers - Acts 1:14), which is interesting because during the period of what we call 'Jesus ministry', they are noted as 'not believing.'
The whole family (most likely) had been engaged in the family business of rural woodworking. Now they were about to make a career change.
It seems that the Apostles organised whatever needed organising in the first days of the early church. They need to appoint some assistants to help organise a daily distribution (and presumably the prior collection of foodstuffs) of food. Interestingly, none of Jesus own family were selected for the job.
Luke's account then focusses on Peter, (to a great extent, the rest of the Apostles then disappear from history) and its after Peter is released from a prison, that we learn something interesting about leadership in the Jerusalem church, for Peter after giving an account of his escape from prison, tells the group he's talking to, "Report these things to James and the brothers." leaving us to assume that in the intervening time, James had gained the most prominent place in the Jerusalem church.