Until the death abuse in Land's End, this guide will note when each character is expected to level up. However the times may not be exact in your run, as you may do things slightly differently. This is a general reference for the level up bonus to choose whenever a particular character levels up in case it happens at an unexpected time.
Mario: All ATTACK except levels 2, 3, 5, 8 do MAGIC
Mallow: All MAGIC except levels 3, 4 do ATTACK (first two level-ups)
Geno: All ATTACK except levels 7, 8 do HP (first two level-ups)
Bowser: All ATTACK
Peach: All MAGIC except level 10 do HP (first level-up)
NOTE: This is only for the beginner route! For level up bonuses for the intermediate No Super Suit route or the WR route, see the Level Up Bonuses page in the Techniques section.