This section moves from chapter 2, which attempts to address what ideal communal worship looks like, to talking about the types of folks who should be leaders in the church. (These also stand right after and seemingly in direct opposition to the authority that is not allowed to ladies in chapter 2.)
Paul tells Timothy that it is indeed a noble task to aspire to be an overseer in the church. This word for overseer, by the way, can be used interchangeably with elder, pastor, or shepherd. There is not a Scriptural distinction for a paid, dedicated clergy and the folks discussed here; same group. What follows is a collection of descriptions intended to show the types of qualities an appropriate pastor has. It’s not an exhaustive list, obviously (and I mean obviously, churches that use this as a checklist would be forced to accept Vlad the Impaler if they followed it to the letter while ignoring the overall picture it paints.) In general, an overseer should be a mature believer whose life reflects being changed by God.
Most of these aren’t surprises. Yes, there are churches that take “husband of one wife” to mean that you can’t be single or divorced to be an overseer. That is an unnecessarily literal reaction to the Greek which straight-read is “of one woman man”. Proper way to read it is probably to mean they are faithful husbands and, you know, not polygamists. This is postured, though, towards fellas and the language does not permit it to be applied universally to ladies as well.
The one about the children tends to be a sticking point as well. What does it mean to say the children should be submissive? I mean, everyone has a kid who is a nut and disobeys in front of other church folk. The follow up description basically explains this as a test. You can BS some of these other things in the list and fool other people. But if all of your progeny are pretentious wild apes, there’s no dodging that. Without being too utilitarian on the thing, I think you can have one who is going through a phase or one of them who is particularly quarrelsome and still be a pastor. But, you know, if your kids are pretty good evidence that you can’t guide them spiritually, you shouldn’t take on the important responsibility of overseeing a community of folks either. No worries, there’s plenty of other work to do.
It also says that you shouldn’t be a new believer. This is primarily because it makes you susceptible to use this power poorly and be taken in by the risks associated with that. (It’s not power in a dominating sense, it’s influence, which pastors should have. It’s also responsibility.) Finally, you should be thought well of by outsiders. It’s not good enough to be the business just within the church community, you’re representing the Lord and His people by this role, gotta do it well.
Next he moves in on the deacons, which is distinct from the elder/pastor/overseer role. The qualifications are much the same, though, except they are not required to be able to teach. (See, there’s hope for you shy bros yet.) Just like pastors, though, this isn’t a political office, it’s an active, working role; a distinction identified by how people treat you, not what title was given to you. By serving others, they gain a good standing for themselves and their personal faith is also emboldened.
The chapter ends with summarizing his intent to teach Timothy how things should be when the Christian community gathers and a reminder that they are the pillar and buttress of the truth (basically, they do the work of holding up truth and sharing the mystery of the faith, captured in the “hymn” that finishes the chapter).