We have a shoe brush hanging from a hook right outside our door so we can stomp and wipe of as much snow as possible before stepping indoors. Usually, we don't use the brush, admittedly, but it is still nice to have when you are just covered in snow that will melt the moment you go inside.
In front of the door outside, we have a metal grill. You know, like a metal mat that you can scrape your boots against. Really good for removing small stones etc.
Stepping inside, we have a fake grass mat. This catches most of the leftover mud from under the boots, and caked on snow from the underside.
Then, as a final line of defence against wetness we have a cotton rag rug, that is machine washable, in front of the bench where we usually sit to take off our boots. Since we grew up with dogs that liked to chew shoes and a cat that when in heat liked to mark them, we tend to put the shoes on a hat shelf, on a metal tray, to dry.