The anime takes place in Cappy Town, where Kirby crashes and learns to harness his inhale and copy abilities, thwart King Dedede and Escargoon's many schemes and ultimately defeat Nightmare Enterprises or N.M.E.
The Japanese and 4Kids dubs make worthwhile watching experiences.
Currently the only readily available, localized, Kirby manga to my knowledge is Manga Mania. A gag manga filled with many hijinks and Kirby getting drunk.
There are however, more adaptations out there that are more faithful to the gams and characters. Not all of them are translated however, so luckily there are some dedicated fans who are willing to change that. You can find a masterlist of current scans and translations here!