Yoshi's Island - Clearly it's best to begin here, since Mario, Luigi, and Bowser are only babies. Kamek, Pooch, and some other enemies are adults or teens.
Yoshi's NEW Island - This is a direct sequel to Yoshi's Island, as Mario and Luigi are being carried to their parents by the stork right after being rescued by Yoshi from Kamek and Prince Bowser. The Stork gets knocked off course, and Yoshi and Mario haft to go through hell to save him and Luigi from Kamek, Prince Bowser, and adult King Bowser.
Yoshi's Island DS - The third game in the Yoshi series is in this place in the timeline
Yoshi's Story - This game is here in the timeline, as Bowser is a tad bit older, and baby Yoshis (who first appeared at the end of Yoshi's Island DS) are now seen constantly.
Mario and Luigi: Partners in Time (PAST) - This is here as the Mario Bros, Peach, and Bowser are now old enough to walk and engage in combat. Bowser also seems to develop a temper towards others around him, showcasing he hasn't grown in personality since the previous game.
Donkey Kong - Cranky Kong is in fact the original DK from the arcade game, and Jumpman is confirmed to be Mario. I also think Pauline is supposed to be the same Pauline from the newer games. I'd say that Cranky in this game is maybe a 30 year old gorilla, and Mario's just a bit younger than him (10-15 years at least). So please ignore what I said in the last timeline please.
Donkey Kong '94 - This game still kind of confuses me, because the DK in this game uses modern DK's looks, but since this takes place before Donkey Kong Jr, as Mario captures Cranky at the end, signifying what's to come.
Donkey Kong Jr. - After Donkey Kong '94, DK Junior (who may be a bit older than Mario as well about 8 or 9 years) saves his father from Mario, who captured the adult gorilla during DK '94.
Donkey Kong 3 - Y'all confirmed that Mario was done with the Kongs after DK Jr, and Stanley's Greenhouse is on an island adjacent to DK island, so Cranky might've gotten lost or something along those lines.
Mario Bros - Mario and Pauline break up, which lets Mario and Luigi focus on their jobs as plumbers, before Bowser gets the idea to send his minions through the pipes, due to all the defeats Bowser had gotten in the past.
Super Mario Bros - Mario and Luigi accidentally go through one of the pipes, witnessing Bowser capture Peach, now the adult ruler of the Mushroom Kingdom, which leads to the brothers rescuing her, and Bowser's defeat.
Mario Bros 2 - The brothers go home, or are staying somewhere, and Mario dreams of himself and his friends saving Subcon from Wart and his minions.
Super Mario 3D Land - This game marks the return of Bowser and the scattering of the Super Leaves. Mario has to save the Princess once again, and also stop Bowser's growing force.
Super Mario Bros 3 - There may be peace for just a little bit, but Bowser quickly retaliates by hiring the Koopalings, and using some of the same tactics he used in 3D Land, like Airships and Boom Boom.
Super Mario World - This game takes place right after Super Mario Bros 3, according the manual. Mario and Luigi, alongside Yoshi go and save the Princess from Bowser and his forces, for a short while that is."