Ayyyyy! Congrats on pulling the true emperor! 
If you want some suggestions, I have a few for sure. But mine are all fairly high-investment, mostly because Edelgard is one of my most valued units.
I have three main builds for her:
- Sturdy Spiral

As @bluebell said, Sturdy Impact works exceptionally well on Edelgard. It’s easier to capitalize on her axe’s Solo effect and it helps her low SPD by cancelling out enemy dou les, buffing her survivability. With her native Slaying effect on her axe, Bonfire has a 2-turn CD, which means that once El fires it off once, she’ll have infinite Bonfire bombs amplified by her Rouse and Brazen ATK/DEF.
I use this build mostly for everyday skirmishing situations.
2. All-In AoE

When her standard Skirmisher build isn’t enough, Edelgard is more than capable of going all-in with massive AoE nuking capabilities. When yoj absolutely, positively , need to make sure something dies, this is the build I use.
Blazing Wind is the AoE I chose, skmply because I prefer the pattern over the other Blazing Skills, that’s up to your preference. LD4 gives her already-high ATK a titanic boost, putting my El’s ATK at more than 70, while also giving her a much-needed SPD boost. And, woth ming at max merges, flowers, amd SS, she still has a respectable 39 DEF before Rouse. Just like with Bonfire, SS means that once she activates her Special, she’ll almost always have another one ready. Rouse is for added ATK and DEF, and Hardy Bearing to prevent Vantage from stopping her.
I have yet to find anything this Edelgard can’t kill, but she risks taking more damage behind enemy lines, especially in modes like GC.
3. Røkkr

This build is more or less maximizing damage while relying on ally support (namely, a healer with a Joyous Staff) to buff her defenses and help keep her alive.
Still needs Repel.