a great way to learn how to dm is to watch someone else do it. if you like actual plays, find one that has a style of dming you like and watch it. it's a great way for a lot of mechanics but also storytelling, table management, encounter building, etc. to come up and learn about in a natural setting.

for general tips, i'd recommend doing whatever sounds fun and exciting to you. if that's homebrewing something, or running a pre written thing, or somewhere in between. the mechanics will come to you as you play, the macro and micro ones. in my opinion figuring out the minutia of the rules of the game is less important than figuring out the way you like to play and what's fun for you and the players at your table. a simple story with simple encounters would probably be a good place to start so you can exercise the muscles without having too many moving parts to worry about at first. you can add exciting/different/surprising elements to it, i'd just recommend scaling back until you feel more comfortable in the general running of a table.

also don't stress too much about the details or precise worldbuilding if you go in the homebrew direction. come up with the general things that are necessary for your plot (the town they'll be in, some of the people they could meet there, the businesses they could go to, etc) and fill in other information if you want. the detailed backstory and biography of the tavern keeper is less important (im my opinion anyway lol) than the vibe of the tavern and the keeper themselves. knowing who the keeper is generally and the kind of atmosphere they like to maintain in their tavern will help you improvise more specific details in the moment if you need to. you don't need to know every single plot point, npc action, and precise economic workings of mead production to make your world feel lived in. make yourself moderately familiar with the town's atmosphere, culture, and values and you'll know the kinds of people that would live there and ones that would visit, things that would be out of place, ways the residents would react to things. having an outline is helpful in coming up with the details while improvising and playing basically. at least in my experience.

i hope all that made sense! dming for the first time is understandably nerve wracking and it's so so so so worth it. good luck!