I think Godot is really good to start with. But it depends on your own needs, I mean if you want to make something that is not supposed to be an AAA-quality, then yes, Godot is the great bet. But if you are about to become a gamedev professional - find a work and so on, - then you should look at Unity/Unreal or even GMS, because seems like those engines are sphere standard now.
I make games just for fun by myself, so for me Godot is a god bless - it is free, lightweight (you are able to run it on a browser even) and stylish.
Yea, the game calculates its battle state first, then, after all calculations are done, it makes saves and, finally, begins playing animations, so reloading the page is almost a legal way to skip battles (but some bugs may occur so I'm not sure it is safe to do in a regular basis) :)