1. Feel free to start with whichever house you want. All three have very strong stories, levels, and characters. If you want the best experience I suggest replaying the game to see all of them.
2. Spend the first several chapters on optional battles. You'll need your party to handle the trickier battles later.
3. When you are exploring the monastery try to spend some time eating meals in the cafeteria. Meals will increase your student's motivation, allowing them to learn more during lectures.
4. Use the terrain to your advantage. Most maps have forests and mountains that you can move to. While these tiles hinder unit's movement, the defense bonuses make them the perfect place to fight enemies.
5. If you have extra time in the monastery, try having tea with characters outside your house. With enough support points they might offer to join your party!
6. Gather as many smithing stones as you can. They can be used to repair weapons if you don't feel like buying replacements.
7. Don't use the rewind function too much right away. You never know when you'll need it.