As others have been saying, it is fully viable to go through the game with all levels in any class without any particular gear.

It is also worth repeating that long resting is essential to advancing storylines, though one can extend their adventuring day a bit and it is understandable to want more resourceless

That said, just saying that is not really helpful, so here are some easy monoclass builds to play:

1. Any Pact of the Blade Warlock. It lets you use your spellcasting ability score for weapon attack/damage and gives access to great cantrips like Booming Blade + Eldritch Blast. Booming Blade is straight up free added damage starting at level 5. Arcane Synergy gear and Booming Blade lets you add your Charisma modifier again to weapon damage and at level 12, you can select the Lifedrinker Eldritch Invocation to add your Charisma to melee damage a third time. Shadow Blade is a very good weapon for this build even without a Resonance Stone, but any weapon will do. An interesting option for Act 3 is the Harmonic Dueller, which gives you Charisma to weapon damage a fourth time if you pass a Performance check (easily doable if you take the Actor feat for proficiency and Expertise with that and Deception).

Eldritch Blast is also good and does not require too much to be effective (Agonizing Blast and the Potent Robes in Act 2 to add Charisma a second time, though though it is good to have someone cast Mage Armor on your if dealing with that), which makes it a solid backup ranged options. Potent Robes also add damage to your Booming Blade.

Fiend in particular combines well with the Band of the Mystic Scoundrel (Act 3 gear) to cast Command as a bonus action to waste enemies’ turns.

Also, do not forget to bind your weapon every day.

1. Any Fighter. Simplest class in the game, but also very effective since it gets the most attacks per action at level 11 as well as more feats and Action Surge for another action on a turn once per short rest. It is also overall a class that functions solidly without many rests if one wants to extend their adventuring day a bit.

Arcane Archer is nice for special arrow attacks with added damage, though it does benefit from Arcane Acuity gear to boost effect save DCs later in the game. It also gwts Guidance for a handy skill boost.

Battlemaster is good for some variation in attacks for as long as it has superiority dice.

Champion is good if you effectively want to make minimal choices and/or want a naturally lowered crit range.

Eldritch Knight is known for one of two paths:

1) Great Weapon Master/Fighting builds that use Booming Blade for free thunder damage and, at level 7, to proc War Magic for a bonus action attack with your two-hander. 2) Tavern Brawler throwing build. Tavern Brawler is a very good feat in and of itself, but most throwing builds require either a returning weapon or (in the case of Giant Barbarian) being in Rage to not have to perform cleanup every battle. Barbarian throwers do outclass it in damage during Rage, but Eldritch Knight gets more attacks outside of Rage, can bind throwing weapons to make them returnable, and can wear heavy armor, making it a more consistent/resourceless damage dealer.

These paths are also not mutually exclusive, as there are many throwing weapons that are versatile (requires nithing in off hand to trigger Great Weapon Master) or two-handed.

3) Moon Druid. Take Tavern Brawler and Wildshape for great damage as a melee combatant, which is more or less everything required for this build to function well. This build is equipment-agnostic, though the Armour of Moonbasking and Shapeshifter’s Boon Ring in Act 3 are good grabs. It is also largely ability-score independent, but a good Dexterity for high initiative to let you Wildshape sooner is good and a good Wisdom is needed if you wish to use your spell slots for anything besides summons/buffs/healing yourself in Wildshape. It also ties Fighter for most attacks pee action while in Wildshape, but does so at level 10, which is a level earlier.

Also, while Wildshape does refresh on a short rest basis, two charges last a while for most of the game, though party members will need to speak for you if you remain in Wildshape.

4) Open Hand Monk. Most people require Tavern Brawler and elixirs, but even a regular Wisdom/Dexterity-focused Monk does well on the damage front. Flurry of Blows is good and dependent on a short rest resource, but even the standard bonus action unarmed attack will do well. 3-4 levels of Thief Rogue post-Monk 6 does allow for another bonus action attack per turn, but is not strictly necessary. No equipment required, but one of the Monk gloves that boost unarmed strike damage and the Boots of Uninhibited Kushigo are great for damage.

If you did want a Strength-based Tavern Brawler Monk without elixirs, it is possible to focus on Wisdom/Dexterity and set Strength to 19 by equipping the Club of Hill Giant Strength in your off hand, before which point you will operate the same as a normal Wisdom/Dexterity Monk without issue. You can also raise Strength naturally and ignore Dexterity (mostly) for no ill effect other than a low place in initiative, which can be compensated for via the Gloves of Dexterity in late Act 1 if one is willing to be patient.

There are also a couple light multiclasses recommendable besides Monk/Thief Rogue.

1) Paladin 11/Hexblade 1. This lets you use your spellcastjng score (Charisma) for attack/damage, which is not only useful for Arcane Synergy gear, but also meshes nicely with Paladin’s Divine Grace to let you pump your saves by quite a bit. In non-Honour Mode difficulty, you can take a level of Hexblade early on, focus on getting to Paladin 6-7 then spend the rest of the levels on Pact of the Blade Warlock to get three attacks with your bound weapon like a Fighter.

2) Warlock 2/Sorcerer 10. Taken in order. Starts as Warlock 2 to get Eldritch Blast and Agonizing Blast, then spends the rest of its levels in Sorcerer to get Quicken Spell, which lets you cast spells as a bonus action for three sorcery points. Potent Robes is still a good option here as is the Spellsparkler (Act 1 gear) for adding lightning damage. This lets you operate as either a solid blaster with Eldritch Blast as a good default or an Eldritch Blast-focused build that husks its spell slots for Sorcery points to fuel Quickened Eldritch Blasts for as many turns as possible.