Regarding the narrative, I wouldn't call it 'tarded, unlike YÜK, but it's definitely meant to be a sillier game than Dragon Quest or Final Fantasy usually are. So you're a boy from Eagleland which is blatantly America, traveling the rest of the US and a few other places in the world, beating up local dogs, hippies, taxis, melting clocks, stop signs, krakens, carpenters, Academy Award statues, and what not. You have psychic powers but that mostly lets you fire psychedelic lasers into the air. There's a bunch of walking potato men named Mr. Saturns who speak in a funny font.
Earthbound and Mother are two different games. Mother is the original NES game, which is somewhat more restricted [it's harder and blander] and the final boss is relatively lamer. Earthbound is the SNES sequel that has similar looking characters [but the new one is from Asia], and the story is technically a sequel but most of what happens in that game doesn't affect this one and it's just referential stuff mostly.
If you can save anywhere you want, Earthbound isn't that bad, since it's harder to make those Sierra mistakes where you might be hours away from the point where you messed up and need to restart, unlike Mother.