Easterners such as Tokyo people use a kind of soy sauce based broth called "warishita" and COOK beef and vegetables in that broth.
On the other hand, westerners, represented by people in Osaka, Kyoto and Nara, say that Sukiyaki historically means "grill on plow", so strongly believe that beef strips which is main ingredient of Sukiyaki dish should be "grilled" with soy sauce and sugar on iron pan.
Me? As one originated from Osaka, I will say it loud;
"you should grill beef! Period!".
It is peaceful battle anyway.
This is traditional (I think) recipe of Sukiyaki.
First, you should grill (or stir) beef on the iron pan with soy sauce(2 table spoon) and sugar(one table spoon). No water added.
After you ate beef, THEN you can add vegetables to the pan where now all the beef juice seasoned by soy sauce and sugar are left. Vegetables contain enough water, so you do not have to add any water unless the pan gets burned.
Ingredient can be spinach, green onion, leek, tohu, sitake mashroom, etc. and my recommendation is konjac noodle. You can finalize Sukiyaki with Udon. Try it!