On a standard hosting (such as an ordinary company web server) you can very simply host your maps. Just upload the Folder (created with MapTiler) to your web hosting and the map is automatically available.
Once uploaded, the produced maps can be opened in any viewer supporting OGC WMTS standard.
For hosting of MBTiles, you can use an open-souce TileServer, that can be used with any standard hosting that supports PHP. Upload the created maps and get dozens of popular web viewers with interactivity, including Google Maps API, Leaflet, OpenLayers, WebGL Earth and MapBox JS.