Team meetings are a necessary evil. They take us away from our work, but if they are run with the right procedures and mindsets, they won't be dreaded time away from work but rather a valued accelerator to that work.
Your team should realize that the key reason you have team meetings is so that everyone can share what is going on. By using transparent communication effectively, people can share helpful resources but also take and share ownership of specific tasks or projects. By placing this communication within a recurring structure, the team is set up for success.
You should have time constraints on your team meetings. They shouldn't be shorter than thirty minutes (you'll be rushing) but they shouldn't run over ninety minutes (it's not a movie). Over time you'll find a time that suits what needs to be covered, but the principle is fit the time around your agenda rather than try to fit your agenda into an arbitrary time.
Each person should get an appropriate amount of time to share what they are working on. This may change depending on projects or times of the year. For example, it's unlikely that a person in charge of sales will speak for the exact same amount of time as a person in charge of finance, but certainly the finance person will need more time at the end of the quarter or fiscal year just like the sales person might need more time before or after a product launch.
This sharing can't simply be a highlight reel. While we want to know what's going well, we also want to know what's not going so well. Again, this is so we can utilize the collective knowledge and power of the team to solve problems or provide assistance. If people can let go of their egos and realize no one expects them to be perfect, they will feel safe sharing their challenges. They won't be made to feel like asking for help is a weakness. This transparency has to be constantly encouraged, and it needs to come from you, the leader.
Speaking of which, you should always make sure you go last. This allows you to have a different opinion, as in group dynamics when a leader goes first, often a majority of the group simply assents to that opinion. Your going last allows more freedom of thought and discussion. It also means you can keep an eye on the clock and meeting management. You're forced to be pithy and pragmatic with your own time.
You can use something as simple as a google doc to document the meeting minutes. The most recent minutes go at the top. This document provides a touchstone and means that there's no confusion about what was said or decided at the meeting. Everyone can access it and even add notes or comments as necessary.
As we've discussed previously, delegation is a key part of your role in management and you don't necessarily need to be at every meeting, or any of them once you've established a strong template. Running a team meeting is a valuable task, but it may not be where you contribute the most value relative to your time. Be open to letting this go once it's well established.