Disclaimer: talking from Unity game development experience.

It is not about resolution...

Base resolution has very little to do with responsive UI. UI elements can be up-scaled or down-scaled. Resolution pretty much only gives you sharpness (or more space if you don't scale your elements accordingly (would not recommend)).

Personally, I choose 1920x1080 (Full HD) as a base resolution. Because it has fairly decent amount of pixels to play with and it used to be a fairly common screen resolution for mobile devices.

... it is about layout and design

What makes UI look good on different sized screens is its design.

For example, you want to make your buttons centered. Writing screen coordinates (let's say X: 640, Y: 480) position will make those buttons look different on 720p and 1080p screens. BUT... if you make them anchor on center of the screen and have offset from it, they will look identical.

What to do?

When designing your UI, think of where it should be placed RELEVANT to something. Let's say, I want my buttons to be spaced at UPPER RIGHT CORNER, I will anchor them to top-right corner and then make positional offset from there. This way, when screen size is changed (aspect ratio and/or resolution), my buttons will still stay at top-right corner.

P.S. apparently @Philipp said the same thing just in other words.

Unfortunately there are so many different devices with so many different resolutions and aspect ratios that there is no one default screen size you can assume. So you have to design your game's UI in a way which looks reasonable well on any device some player might own. You will have to create a responsive layout where UI elements are positioned relative to their closest screen corner or screen edge center and which scale with the device pixel ratio. Then you have to continuously test your UIs with lots of different screen sizes to make sure the layout works on any one.