Journey

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I'd suggest going for Quick Journey as soon as you get it. 
Once you are at a high Honor Title (around Marquis), you should switch to Manual Journey because these monster battles will give you much lesser honor points (1-6).
Here's the explanation:
* You spend a significant amount of time doing manual journey, only to get 12 honor points. You can't even choose the loot you get.
* With quick journey, you save the time of doing manual journey. It yields 0 honor points, but you use that time to do more quick journeys and fight more monsters (fight monsters faster than manual journey, and yields 12 honor points at the start). 
* Thus, you should be able to grind honor faster this way. Plus, you get to choose your loot.
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Quick Journeying gives no honor points, but it's much faster, and you get to choose the kind of dungeon you want to visit (and hence the drops you'll get). Did I mention it saves time? It's a one-click button that finishes your explorations quickly.
Let's count the steps involved:
* Click the button. -> Short processing screen. 
* Click "accept" on loot. 
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Manual Journey gives honor points depending on the dungeon your invade (more on that here). It's highly useful after Marquis because most monsters will give you 1-6hp. At Emperor everything gives 1 honor point, other than dungeons. 
Let's count the steps involved:
* Click the journey button.
* Select if you want to journey or cancel. -> Moves to loading screen
* Click on "Dungeon Info." Select a dungeon (takes a second or two to decide if you're at a high honor rank), click "Inspection". -> Short transition screen.
* Click Attack. Moves to the screen where you can select your team. Click Fight. ->Loading Screen.
* Skip Fight. See Result. Click anywhere on screen. -> Loading Screen.
* Click Anywhere on screen to accept loot. Done.
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This section is for completeness.
* Click on monster. Click Capture. Click Fight. ->Moves to loading screen.
* Skip Battle. See Result. Click anywhere on screen. -> Loading screen.
* Repeat steps until all the monsters that give you 6+ honor points are dead.