I would
very much caution against Made in Abyss. It has its following, but it's certainly not a "newbie" series and it can be several shades of disturbing.
There are a lot of possibilites, but at the top of my head there are two standout examples that I'd call "newbie friendly" and meet your
superpowers criteria:
A lot of fans of the medium were introduced to it with
Dragonball (and its sequel series of Dragonball Z), and its hard to overstate its influence on the medium, its genre, and global pop culture (to the point that it's frequently cited as the largest influence in making Japanese animation poplular outside of Japan). Very much an adventure and fighting focused series, with the major conflicts all employing martial arts at superhuman levels (super speed, super strength, ki blasts, etc). As an aside, if you do go with this, when you get to the Dragonball Z portions, I would highly recommend looking for Dragonball Z
Kai, as it's a remaster of the original DBZ which redubs the series with better voice acting, cleans up some of the animation, and cuts out a
lot of the padding.
Fullmetal Alchemist Brotherhood is a personal favorite, and one I'd consider pretty easy to get into. This is a remake of the Fullmetal Alchemist anime that aired in 2003-2004, which quickly overtook the source material and then ended up going in a completely different direction. I personally recommend Brotherhood because I prefer Arakawa's themes, but acknowledge that FMAB kinda glossed over and speedran the first few stories that it had in common with the first anime. Plenty of action and applications of
magic powers, but a bit more mystery oriented than Dragonball.
