---Visit all the Prayer Boards in all four regions before taking on monsters (unless they require items you don't have), best to start strong.
---Luxerion South Station is where you'll do most of your Teleporting for quests in the beginning. The other areas would be Jagd and Wildlands Research Camp for shops. For Luxerion quests, 10:00 am, 16:00 pm, and 0:00am are the best times to talk to people and get stuff done, for the "ghost quest" you need to talk to 4 different people in the morning before the 3 ghosts show up at night.
---Caius (Wildlands), Goblotts (Dead Dunes), and Gremlins (Luxerion / Wildlands) don't change/enhance their item drops after Day 7, so it's okay to extinct them early on or later as you please... ideal for planning your routes in the game. Caius in particular does NOT get stronger as the days go by, so you can use him to kill time between bosses and earn stats/weapons/whatever or to farm Meonektons in the temple for Gil/EP/Ruin spells/whatever.
---1600-1800 (4pm-6pm) and 0400-0600 (4am-6am) are the best times to go out on quests if you're avoiding other monsters for better drops until Day 7 or Day 10. Monster drops improve on those days, but equipment in shops improves on the days after (Day 8 and Day 11).
---Your last Prayer Board missions show up after Day 9, which is when the Roadworks roads can be opened for Chaos Infusions (which is required for some rare abilities outside of rare synthesis, in fact there's an Omega exclusive infusion with a Goblin Last One that needs it).
---Once you get all your items (Head Accessories) upgraded from the 3rd Cycle, Item Spheres drop Gil and EP Item Spheres drop LOTS of Gil, so even if you already spent your EP before, every cycle is a good time to get more (at least until you buy all the garbs). So save up and get those Turbo Ethers from Online people! If you don't want to spend EP there's always Cactuars.
---Head Accessories are Garb Specific while Arm Accessories affect all three Schemata, so plan your combinations accordingly. Having accessories that boost elemental damagecombined with Enfire/Enthunder/Enaero/Enfrost etc is very helpful (especially once you get stuff like Elemental Chaser later on).
---Only a small group of monsters in the game drop Element / Elementa / Elementaga per cycle, so make those synths count and save beforehand. That goes for other rare spells as well (make sure you synth same abilities early on to different spells so that you can make rare synths).
---Once you've beaten the game once, Mog will have everything (except adventuring essentials) from the Final Day in his shop. If you don't have the Gil for his stuff, kill some Set monsters as they drop Executioner's Axes that sell for 9k gil a piece.
---Assuming you plan on extincting every monster before/during Day 13 know that it takes about half a day (0600am-1200pm) to clear the Ultimate Lair when there aren't any monsters there on Easy Mode so plan to spend EP to preserve the time afterwards. In Ultimate Lair, Meonekton is on floor 16 (which can't be avoided because the warp system teleports in multiples of 3, usually the Lair is mostly empty when I visit because I extinct most monsters before I visit the place). Cactuar Omega is on floor 17 so avoid it by warping if you plan on farming his buddies for Gil on the 13th day. Make sure you extinct the 3 monsters Neela (Sugriva/Wendigo), Arcangeli, and Chimera in the Final Day to clear the quest the next time you visit the old man by the Light House.
---Accessory drops from Last Ones will give you either an Accessory upgrade or Gil on subsequent pickups (unless the item is a weapon, in which case you could sell it for Gil or Upgrade it and sell it). Here's how it works depending on the drop:
---Head Accessory > + > ++ > Gil
---Arm Accessory > Gil
---Weapon > (another Weapon you can sell).
---Don't forget you can sell / rebuy DLC items at any time. I sold my Aegis shield for a hefty sum to get the Masamune before I was supposed to get it! Also note you can't sell to Online people, only in-game merchants. Also the items you upload online won't give you gil when they buy them.
---Don't forget to mark key quest points on your map for subsequent cycles (EP treasure, Rare Forge locations you spot him in, Lost Moogles, Gold Dust drops, Crimm Mushroom locations, for time-sensitive areas in the Dead Dune Ruins mark the treasures as odd hours or even hours so you know when it's good to come and pick them up, etc):
---Red Markers for Rare Forge/Red Treasure Chests/Crimm Mushroom/Music Chests
---Blue Markers for EP chests, Drop Respawns, Key individuals, Chaos Infusion spawn points.
---White for Moogles/Gold Dust/Rocky Crag Moles/etc.
---If you have the Gil to spend, it's worth it to buy all the different types of weapons/shields as "fashion accessories" to your schemata, as no matter which "grade" of weapon/shield you buy, they all end up with the same stats when fully upgraded, so even a weak shield that looks cool can have the same stats as a shield that doesn't look as great but works better. Even cooler, if you can buy/upgrade multiple copies of a weapon and shield, you can use it on different schemata that it looks good with.