Starting out as weak. Later on, it depends.
Sometimes we don’t want a power fantasy. We want our main character to start out as weak as possible, and without any Deus Ex Machina shortcuts to the top of the food chain (looking at you, That Time I Got Reincarnated as a Slime (Tensei shitara Slime Datta Ken). And, here are five anime that offer exactly that:
1. Spider’s Insane Difficulty survival
If you still want a battle series, but with the main character being at an enormous disadvantage from the start, So I'm a Spider, So What? (Kumo desu ga, Nani ka?) has that in spades. MC is reincarnated as a weak spider monster in the most dangerous dungeon in the world, and is dragged kicking and screaming through a gauntlet of increasingly deadly opponents.
She does get very strong later on, but unlike a certain cheating slime, she has to pay for every ounce of that power with blood, sweat, tears and sanity. Usually, her own. Also, you might want to read the manga, rather than watching the anime.
2. A handyman is a great substitute for a Thief
If you still want adventures, but with less of a survival aspect, Handyman Saitou in Another World (Benriya Saitou-san, Isekai ni Iku) offers a more measured isekai experience. Saitou is a professional handyman who gets isekaied into a fantasy world, and finds his skillset pretty damn useful in an average party. He doesn’t get much stronger, though he learns skills and tricks to make his party way more efficient.
And the best part is that unlike many anime’s Hero parties, his teammates appreciate him.
3. Cooking with modern ingredients in medieval fantasy
Campfire Cooking in Another World with My Absurd Skill (Tondemo Skill de Isekai Hourou Meshi) also offers its own share of adventures — this time with an MC named Mukouda who has a kind of a cheat skill: through a menu, he uses that world’s coins to buy anything that could be found in a convenience store. He’s also a pretty good cook. Thanks to this, he rapidly amasses a following of extremely powerful (and epicurean) beings, and obtains blessings that make him somewhat decent in a fight.
Still, even with all these blessings and powerful backing, Mukouda is kind of a pushover. Not that it matters much, since this anime is mostly about cooking.
4. Saving the world through kingdom management
Imagine being summoned to another world to save it from the Demon Lord, and you don’t even have a cheat skill. How a Realist Hero Rebuilt the Kingdom (Genjitsu Shugi Yuusha no Oukoku Saikenki) is about Souma Kazuya — a man with a weird and unironic fixation on Machiavelli’s “The Prince” (which was meant as a political critique, rather than a guide). He uses his political and managemental acumen to save the kingdom from the brink of collapse from debt, wars and natural disasters.
So, this story is basically “What if Rimuru wasn’t overpowered”.
5. Making books (gone political)
The main character of Ascendance of a Bookworm (Honzuki no Gekokujou: Shisho ni Naru Tame ni wa Shudan wo Erandeiraremasen) starts out as underpowered as she could possibly be — Myne is a little, sickly peasant girl barely able to walk across the street without getting winded. She’s a book enthusiast, reborn in a world where only nobles can afford books — so she decides to make books on her own, slowly but surely approaching her goal step by step.
Later on, the story gets into the matters of management, religion, magic, and politics. Myne is revealed to have a LOT of magic power, though she’s still frail and sickly multiple seasons in. Also, this series has so few fights in a season you could count them on one hand of a veteran sawmill worker.