Hire manager-of-one types of people that don't need hand holding to get their job done. Don't worry that your staff want your job, many of the senior software people do not want management at all.
See yourself as part of the team with the unique position of gathering information from experts, coordinating and depending on your responsibilities care for the well being of the team and the development of the individuals in it.
About tons of priorities: Here I struggle more myself, because I'm not in the position to delegate much of my own work.
What I do: I write down everything (for me it's org-mode, but that's a matter of taste). This includes tasks of others I delegated (in my system marked as WAIT). ~10% of my tasks are marked as high priority.
This waiting thing however drives me mad. Within my team we use a ticketing system and things get done, but I constantly have to do things with ~7 people outside of my department and have to run after them constantly. Even if they have to-do tools where I make them tickets. I'm at ~30 todo items (that's low for me) and ~70 waiting (that's normal).
- You can't do everything and you can't do it perfect every time but you can try your best every time.
- People you work with are older, smarter and more experienced. So make use of it, ask questions and make it clear that you are willing to learn everything where you lack knowledge.
- Look out for people who have certain capabilities which you would like to adopt. For example how they interact with a customers or how they organize tasks. Observe how they do that and what their workflow is. Try it and figure out if it fits you too. You can also ask for tips as these people had to figure it out too.
- Reflect. After some time look back at your work and figure out where things went wrong. Change your workflow to avoid that it happens again.
- Everyone wings it on an everyday basis, so you can do it too.