The rewards that my kids are most excited about are the ones that they choose. We create a choice board, similar to the menu you shared, with their suggestions. I even have a blank template and they actually build our choice board! I taught Kinder at the time and we made it part of our interactive writing. They loved being part of it!
Some of their favorites were so simple…
Take off your shoes for the day (class period, reading time, etc.)
Switch seats
VIS very important student with a special desk and supplies
Bring a stuffy
Eat lunch outside
Chew gum during math
Sit by a friend at lunch
Tell a joke during school announcements

I also use student chosen rewards. We use a warm fuzzy jar in my kindergarten classroom, and when we fill the warm fuzzy jar, students share out different ideas about how we can celebrate. In the past, those ideas have included more recess time, extra playtime at the end of the day, watching a short movie or TV episode (all appropriate for five and six year olds), reading in the dark with flashlights, having their teacher or a special guest reader read five or six books back to back, wearing pajamas to school for a pajama day, and our favorite has been drawing on paper that has been taped to the underside of the tables.

When my students are able to choose the reward, that makes them even more excited about filling up the warm fuzzy jar next time! After all of the suggestions have been shared, each child gets to vote for their favorite and the choice that ends up with the most tally marks, is chosen.

Sometimes, if we have a bit of extra time, I am able to squeeze in two of the choices. For example, the last time we filled the warm fuzzy jar my students voted for a pajama day, however, reading books in the dark with flashlights only lost by one point, so we were able to do both in one day.

I agree with the student choice as a reward. We also set goals to meet for the class. I my class, we have competitions to encourage an “iron sharpens iron” type of deal. The main thing is to keep it fresh and interesting for the students. If it becomes routine the students will lose interest.