For layout type things like the sizes of boxes, you want to use % because you will typically have several columns sized as a percentage of their parent that will stack on top of each other at a certain breakpoint (width:100%). No other unit will allow you to fill 100% of the space like % does.
For padding/margins use em, normally you will want to space your elements out relative to the size of your text. With em (the with of an ‘M’ character) you can quite easily say I want approximately 1 character spacing here.
For borders you can use px or em, there is a difference though. If you want your border to look like it’s one pixel wide on all devices, use 1px. It may not be one pixel on all devices however, high density displays convert 1px into 2px for example. If you want your border to be a size based on your font, use em.
For fonts use em (or %), the use of em carries through parents to children and it just a nicer unit to work with over px.