In iOS platform , XCode is best.
XCode is developed by Apple .so Apple optimise it several years.
In Android platform . There are various choices.
Android Studio ,You can try it .
If you can use others languages fluently.
E.g Node.js ,It have lots of frames can work on Android & iOS platforms .
In my opinion ,i don't think any SDK is best.
I think the best SDK are what your use best.
By the way , design inspriation,
I can't help you , But you can find them anywhere.
Before you write your the first line of code, You should consider twice .
1) Who will use my App
2) Worth of my App
3) Features of my App
This is my first port.the typesetting is poor , Sorry