Consider the dough your palette: flavor it any way you like. In my experience, if you want the children to love these, you better leave the anise out. For the syrup, use a combination of rose water and orange blossom water, or just orange blossom water, for flavoring.
In a small heavy saucepan, combine sugar, water and lemon juice and bring to a boil over medium high heat. Reduce heat to low and simmer for 5 minutes.
Remove from the heat and add the orange blossom water and rose water (measure away from the pan so spills don't happen in your syrup!).
Pour the syrup into a heatproof container and refrigerate to chill completely.
Use a stand mixer fitted with the dough hook, or mix by hand. In a small bowl, mix the yeast with 1/4 cup of the warm water and 1 tablespoon of the sugar. Let this stand until it is creamy and a bit bubbly, about 10 minutes.
In a large bowl or the bowl of the stand mixer, combine the flour, remaining sugar, salt, anise, and cinnamon. Add the proofed yeast and mix by hand, or with the dough hook on the mixer, slowly adding the remaining water. Knead until the dough is smooth, sticky, and soft.
In another medium bowl, coat the interior of the bowl with the teaspoon of oil. Place the dough in the bowl, coating the ball of dough with the oil. Cover the bowl with plastic wrap (without touching the dough with it), cover that with a kitchen towel, and set aside to rise in a warm spot for 90 minutes.
Deflate the risen dough, cover again with the plastic wrap and towel, and let the dough rise again for 30 minutes.
Fill a nonstick frying pan to about an inch high with oil. Heat over medium heat to 370 to 375 degrees.
Pull off walnut-sized pieces of dough and shape them into balls. Place the balls on a lightly floured sheet pan. The shape of the balls don't have to be perfect!
Set up a rack over a sheet pan next to the frying pan. Fry several balls at a time, taking care to cook them through before the exterior is browned by adjusting the heat down as needed. Flip the balls over with a slotted spoon, then remove them when they are golden brown all over and place them on the rack.
To glaze the donuts, pour the cold syrup over the warm donuts, or dip the donuts in the syrup. Serve immediately with additional syrup for dipping.