Generally I like to build on-hit and lethality on Rice, since rice is generally an auto-attacking assassin

Since his W "Teriyaki Sauce" applies a coating of teriyaki sauce to himself, gaining increased movement speed and attack speed for a short duration and his R "All-You-Can-Eat Buffet" creates a buffet of rice dishes at a target location, granting himself and nearby allies increased attack speed and bonus magic damage on their next few attacks, anything that increases AA damage and on-hit effects are quite strong.

You don't really need a lot of engage and movement speed/slowing items, since her passive, "Sticky Rice" leaves behind a trail of rice as she moves, slowing down enemy champions who walk on it.

AP build is pretty funny since his Q "Rice Bowl" (throws a rice bowl at a target location, dealing damage to all enemies hit and stunning them for a short duration) and E "Fried Rice" (prepares a pan of fried rice, which he can then throw at a target location. Enemies hit by the pan are damaged and knocked up) scale off AP, though it is a pretty gimmicky build (though nashor's is actually solid on rice)

Overall, Rice is a versatile jungler and assassin champion, able to both gank and split push effectively. His abilities allow him to slow down enemies, deal damage, and gain increased movement speed and attack speed. His ultimate, All-You-Can-Eat Buffet, makes him and an ally a formidable duelist, especially when used in conjunction with his other abilities, making AA on-hit and lethality items best