Constructive criticism is preferrd
I recommend Katekyo Hitman Reborn with some caution as the series is really goofy at times and can get a bit annoying at middle of arcs.
Katekyo Hitman Reborn tells a story about spineless and useless Sawada Tsunayoshi and his involvement with the "mafia". Start of the series is really comedic and most likely was intended as gag manga as in manga all of the really slice of life/comedy parts were in one arc taking up chapters 1-60. In anime first 19 episodes are the comical part,with some small stories being in between first 3 story arcs. For those who do not
like comedy I wouldn't recommend this anime but even if you are ok with comedy I would recommend starting from episode 19.
Characters are introduced precisely in the order of importance at least for the main cast Reborn(the "infant"), Sawada,Gokudera,Yamamoto, Hibari and Ryohei.
Majority of the story revolves around Sawada,10th head of mafia and Reborn the infant hitman. The guardians (rest of previously named characters and one villain ) are constantly present at the story but the focus is rarely on them.
For the actual story you could say the arc starts with Sawada being reluctant in taking the mantle of 10th head of mafia. Then suddenly enemy appears and defeat the guardians and it's time for some power ups. After the power ups the guardians defeat their corresponding enemy usually and Sawada defeats the big boss. End result everything is fine but the enemy becomes their allies for the rest of the arcs. Regardless of the linear plot of arcs each of story arcs is enjoyable.
On larger scale the plot is really full of plot holes and contradictions. Some are later commented at manga but most are just let unattended. The longest,best and darkest of arcs is the last of arcs in anime "Future arc" but instead of fixing any contradictions made earlier it makes just a load of new ones for example new gadgets and combat system. Meaning of elements and their interactions for example.
On visual and sound side of things Katekyo Hitman Reborn! is great. Sounds sound great and visuals is great , combat in the future arc gets slightly worse grading from me, maybe for the combat system but I really don't like firing beams in anime and it wasn't really well done.
Overall I would give describe comical shonen series with it's fair share of twists, plenty of near meaningless fights and even less clear power ups. Bit series does keep you entertained and amused while watching Reborn.