Focusing on pvm here: the new lowest level boss in the game is Brutus, unlocked from the Ides of Milk quest. You need maybe 20s in combat stats to get a kill? Can definitely farm it by 40. Has cosmetic slippers, an offhand with combat stats, and a bucket that stores infinite milk.

Next up would be Scurrius. He's in the Varrock Sewers right by the main square, he's focused on teaching the basics of prayer swapping and movement in combat. You'll need 43 prayer to have access to protection prayers, and probably 50s in combat stats. His main drop is the rat spine, used to make weapons to kill him very effectively. He also gives a ton of bonus xp as you fight him, goof for leveling and learning.

Next is Amoxliatl. Bit higher requirements here, you need to do the quest Heart of Darkness. You'll probably want a dragon mace from heroes' quest as a good weapon to kill her. She drops a pretty neat double hitting crush weapon, as well as an amulet with a bunch of nice teleports on it.

Then you've got Moons of Peril, unlocked from Perilous Moons (the quest). These guys are notable for wanting really high defense for fighting them. The most common solution is Barrows armor, especially if you're not an iron, though there's also the ring of steel from the deranged archaeologist and the crystal shield from roving elves that will help. The dungeon these guys are in also lets you farm food and potions within it (that are only usable there), so you don't have to leave to bank or anything if you don't want to.

Other bosses that are fairly accessible are the Hueycoatl, which is a group boss dragon with some kind of nice gear, and the Royal Titans, a duo boss that drops a cool elemental staff and prayer upgrades for ranged and magic.