Removing ways which only have either a building tag, a building tag and a source tag or a building tag, source tag and wall tag will **significantly** reduce the file size. On the other hand, nominatim might do this already. You'd also want to remove their nodes if you're not planning to use updates.
You can't always remove roads because they're important for geocoding. some geocoders rely on them.
From a file size perspective, the planet is largely buildings, roads and the nodes used for them. natural/landuse are the only other tags that spring to mind, but you don't want to removed any named landuse.