I have found over my months of playing this rando that the start of the seed is the hardest. Then at some point I find something that cracks the seed open for me. I think it is also where many people struggle. So here is how I start a seed, on the standard racing or Battle Royale flags. Usually by the time I have done these three things I am good to go and start rolling through a seed.
Loot chests: The first thing I do is I gather chests. I will always loot South Figaro and Narshe. Then if I have Terra I will go loot the Imperial Base and the Cave to the Sealed Gate. If needed Albrook is also a good option as it has 5 items (note this map shows the two chests in the armor shop as open, they are filled with goodies in the rando.) Note about all of the maps: they list the vanilla chest contents. I linked them so you can see all the locations. At the start I am looking for a few things: offense, defense, healing, utility.
Offense: Here I am looking for rods (fire, thunder, ice, or pearl), elemental shields, fixed dice, end game weapons (Illumina, Ragnarok, Excalibur, Sky Render, Aura/Pearl Lance) and super balls. Any of these will help me get through the first few checks and get me rolling.
Defense: WALL RING, elemental shields, force armor/shield, aegis/genji shield, Minerva, Red Jacket, Snow Muffler, Ribbon. Wall ring is particularly important since a wall ring can either outright win a tough boss battle (Magimaster) or make some of them easier/more manageable (Poltergiest, Doom, Phunbaba, etc.) Elemental shields, Minerva, Red Jacket, and Snow Muffler all offer some elemental nullification/absorption. Snow muffler, in particular, offers a huge amount of physical defense. Ribbon protects against all status effects.
Healing: Elixirs, potions, tents, sleeping bags, ethers, Fenix Downs. Gotta keep the team up until you find some more reliable healing/magic.
Utility: Status healing items (remedy, softs, echo screens). They are at the bottom of what I am looking for, but can be useful in the right situations.
Shopping!: While I am checking these chests in towns, I am also checking the shops. I am looking for mostly the same things. Mostly I am looking for offensive items and healing. If there are rods in a shop I will sell what I have to pick them up. I also try to pick up 15 or so fenix downs, a couple of revivifies (to one shot undead bosses such as Phantom Train, and Hidon), a single dried meat (for Gau’s check). I am on the lookout for a wall ring. Otherwise if there are any of the items from above that I hope to get from chests they are on the list of things I will consider buying as well.
Free Checks: Then I am looking to do my free checks. By free I mean without fights. Free checks; Sealed Cave, Collapsing House, Gau Manor, Kholigen Inn, Zone Eater, Celes’ Cell, Mt. Zozo, Lone Wolf, Gau on the Veldt, Figaro Throne, Phoenix Cave, Narshe Weapon Shop, sketchy guy in Tzen. The auction house is technically free in terms of battles, but it is so random I usually avoid it.
I do these checks looking for: espers for magic, offensive items, and characters for progression. The spells I am looking for are: tier 2/3 elemental spells, flare, pearl, ultima, healing spells, life spells. Meteor can be decent early. I am also looking for espers for stat boosts (these are nice but not necessary).
Finally, one of the most important and underrated things is that checks with espers and characters will raise the level of the enemies. This will make them give more experience points and make it easier and more efficient to level up.