Stay. A website can be done by setting the percentage sizes and fixing what to break with the average queries.
However, making a site responsive through% turns out to be somewhat cumbersome and laborious.
You would need to work each element with a relative size because it would be a percentage relative to the monitor.
One of the alternatives is to use frameworks that already do this for you through classes such as Bootstrap, Wirefy, Skeleton, Less Framework, and so on. (In the end, these frameworks use everything in percentage.)
Aspects: responsive images that fit the screen size, accessibility (thinking that the user can use the touch on a small screen instead of a mouse), etc.
According to the book Responsive Web Design: Adaptive pages for all devices, the crack for responsiveness is:
- Flowing Layout: think from layouts to layouts that are not fixed in size, and can be tailored to prevent content from being cut or create scroll bars;
- Flexible imagery and features; and
- Media queries: directives where you can hide, make appear and reposition elements and interactions according to the current resolution being used at the time of visitation. After all, a website does not need (and should not) exactly have the same look and layout of elements in any resolution.
Reference: ZEMEL, Tárcio. Responsive Web Design: Adaptive pages for all devices. Publisher Casa do Código, 2015. link