In D2 probably easiest, most item independent was Necromancer summoner. Until hell difficulty, there were nothing difficult at all. You summon a bunch of skeletons, some mages, enemy monsters themselves (revive skill) and a golem (clay one probably was best) and get skeleton upgrades. Mostly they do physical damage (except skeleton mages, which aren't so powerfull), so to avoid physical immunes or highly ressistant in later difficulties, you could have cursed with decrepify (-50% physical resistance and some slow or amplify damage -100% physical resistance). Items even though could have made it a lot stronger, but were good enough even the ones, you found yourself. If by some luck you get exceptional unique trident for your hireling, then such boss like Baal, couldn't even move at all during the fight (he would be too slow to teleport and that wouldn't require mana for decrepify), although you can get enough mana potions and use it yourself.
Casters however (sorceress, paladin with hammer, necromancer with bones/poison), had probably easier time killing specific monsters and did that faster, however their survivability was not high enough.
Sorceress had teleport, without which she would have been useless even with high damage. However hell difficulty even with it is not easy. You can get one skill which is your main one (meteor, firewall, etc) and another which is great by itself (frozen orb). So you could pretty much kill everyone (if not - hireling + static field until 50% hp). And teleport made it easy to skip bunch of immunes, which were not required to kill.
Paladin had skill, which was so powerfull due to monsters not being immune to it (except very few). To be effective with your found items, you needed some skill to be fast just in case (charge), to have someone to tank without you (mercenary) and to master the pattern of hammers. Then slowly you could reach the end of hell. Bosses however are deadly to this one (Duriel, Andariel, Diablo). Need to search high +resist items to survive against them, because especially against Duriel, you couldn't use surroundings for your advantage (he would often charge at you and kill) and kill pretty quickly.
Druid - a weaker summoner however also quite viable until hell. Even there he is pretty tough, however against physical immunes... He was weak (exceptional unique trident was a must and even with it you couldn't kill ghosts).
Of course it is possible to beat hell with any class, but it takes lots of time to - farm items youself for a while, die a lot against strong enemies, skip some too powerfull enemies.
However you remember hammer paladin (especially him), summoner necromancer weren't such builds, which everyone played from the start of the game, because people didn't realise the potency of them? So tip for Diablo 3. Take a deep look at skills, game mechanics and try to find the best way to become strong overall - not to level up skills, which might have problems later on.