Well, I know it may seem like a long way to go, but an adventurer like Mikoto really deserves a 5* 3rd tier weapon. I have 12 nat5s and the only ones I have bothered to build a 5t3 weapon for are ones I’m planning on using for the advanced dragon trials. The mats are hard to come by, but you’ll feel a lot better once you start progressing towards that end game content.
Teamwise you’ll get most 4*s you need as you start to pull on banners. Try to complete every event and get all the goodies. You’ll have more than enough mana and gold as time goes by. Unless an event has a devastating status ailment you need to protect against, you can get away with your best adventurers + a healer in most raid content. I have a 20k + might team and I don’t mind running with whoever, whenever. The only time you should get Noped is in advanced dragon trials (most of the time).
Just have fun. Use your materials wisely, always feed your dragons, and finish events. You’ll be progressing towards HMS with Mikoto in no time!!