While moving forward in the game is obvious, you can also move backwards whenever you need to. Hit an old stage and auto-battle it to complete it instantly and load up on items and equipment. You can either farm the most recent level that you have completed in orer to maximize experience points, or you can move from level to level to get a wide variety of different equipment and items.
Equipping your party is done automatically by the game, which picks the highest-powered equipment. Still, though, go through the equipment anyways to make sure that there isn't a piece that the game overlooks or that fits your style of play better than what the game thinks will fit.
One of the most basic ways to manage your team is to put everyone in the right positions. There is no difference in how melee or ranged characters will perform in one position or the other; instead, heroes in front are attacked first, and back last. Stick your highest-defense heroes, your tanks, in the front so that they can suck uiuop a ton of damage. This will maximize the time that you'll be at maximum strength for.
You'll get a ton of heroes that you don't need as you go, so you can sacrifice them at the altar to get even more equipment and other goodies. Or, you can used the Fused Quartz, which earns you top-tier heroes in exchange for multiple slightly-weaker rare heroes. Don't use the fusion too early on in the game though; wait until you have a good stash of rare heroes, so that you don't end up with 1-3 stars in your party to replace 4-5 star heroes.
To get a ton of extra loot, make full use of the quests. Hit the pub and put a hero on a quest and they will auto-complete it within a certain amount of time. the best part is, even if a hero is on a quest, they can still be used in your party as an active party member.