Once the early chapters are behind you, progress comes from the systems around the run rather than the run itself. This is the order to invest in, reworded from the game's own systems.
Gear
You wear 1 Weapon, 1 Shield, 2 Rings and 2 Gloves. Whatever you equip is dragged into the backpack as starting items each run, so good gear is a permanent head start.
Level gear slots with Gear Enhancement Stones; every 10 levels a Gear Blueprint is required before you can continue, to a max of 80. Swapping the gear in a slot keeps the slot's level, so upgrade the slot, not the piece.
Upgrade a gear piece's grade by merging copies of it — Common through Mythic +4. Resetting a '+'-upgraded piece returns Gear Scrolls you can spend on other gear in the same slot, so nothing is lost.
Dragon's Blessing
In the Dungeon tab. Spend blessing gems — Courage for Warrior, Agile for Ranger, Wisdom for Wizard, 10 per attempt — to roll a blessing from Common to Mythic.
The overall Dragon's Blessing level (1 to 9) raises the odds and the rarity ceiling and unlocks blessing slots up to 5. Push the overall level before chasing perfect individual rolls.
Each blessing shows an effective percentage next to its rarity — how high it rolled within that rarity's range. A high-rarity blessing that rolled low is still worth re-rolling.
Pets
Up to 3 per run, from the Nest using Pet Eggs. Level them with Pet Food (max 80) and rank them up with Pet Shards.
Ranking improves the ownership effect and can lower the activation cost. Because you only have 5 points of pet budget per run, a rank-up that drops a pet from cost 3 to cost 2 effectively gives you another pet.
See the Pet section of the Tier List for which pets are worth the shards.
The daily routine
Spend energy on Chapter Challenge (5 per run) and clear the daily dungeons — Pet, Hero and Blessing — for progression materials.
Tower of Trials tickets regenerate one every 10 minutes up to 10, and clearing a boss sub-floor grants 10 more plus Gold Keys. Clear at least the boss floors each day so tickets don't cap and waste.
Claim Expedition rewards before the 20-hour cap, and take the free quick expeditions.
What each mode is for
Chapter Challenge — main progression, gold, and stars (every 3 stars = 200 gems).
Tower of Trials — Gear Enhancement Stones and Blueprints; a pure test of your build since you can't shop mid-run.
Dungeons — the only source of hero / pet / blessing materials. Do them daily.
Arena — Medals of Honor for the Arena shop; uses separate backpacks, so it's its own puzzle.
Clan — donations for Clan Coins and the Clan Shop, plus Clan Raid.