In my laptop (16 GB RAM 512 GB SSD i7-8550U) I could manage the entire South America with rails app (osm website) and tile server with pre-rendered tiles up to zoom 11 and I think there were still room for more data.
But if you want to pre-render up to the max zoom you will probably need more space.
You can check it here http://tools.geofabrik.de/calc/