Liurnia is best done right after Stormveil Castle. It's typical end content is the Academy. The goal is to clear most of the open-world content (including Caria Manor and Ranni’s quests) before the Academy. Full Ranni quest requires defeating Radahn, so you’ll naturally progress into Caelid as well. I am unsure if you really need to kill Radhan before finishing here, but let's worry about that as late as possible.
Step one is basically to run around and get as many waypoints as you can. You can even get to Bellum highway if you explore long enough, but the immediate pick-ups are Land Squirt ashes, Raya Lucaria Crystal Tunnel, Road's End Catacombs, and the Academy key beside the dragon. Also try to get to Smithmaster Iji. To do this run around the eastern and then western shores of the lake, then run up the west and east cliffs to explore the plateaus. If you really want to prep then go to Sealed Tunnels and Ariza Hero's Grave for smithing stones and Ghost/Grave gloveworts and armor. Then it's Liurna time.