Planning to buy a compact camera for my girlfriend. Any tips?

So for a while I've planned to buy a camera for my girl as a birthday gift. She has no experience in cameras and neither do I. I researched a bit and thought that a simple compact camera, like sony rx100 or lumix tz 200. What is a good, and relatively affordable compact camera with a budget around 500-700 euros? And is that even a good choice? Thank you all.