Use warm water, dish liquid and a bit of baking soda. Use a damp only mop and leave no excess water as to make streaks.
Once and Done is a product I get from Home Depot or Lowes it does a great job and if you follow instructions on the bottle (it is concentrated) it cleans and shines tile, vinyl and laminate flooring
Damp mop and floor cleaner
I like a steamer for tile.
The vinyl plank should have had cleaner recommendations, if you know the brand go to the website and you should be able to find out. Most all vinyl plank is pretty moisture proof, myself, I would just try warm water and damp mop. The steamer on the tile is a good suggestion, it dries quickly and with less streaking.
And after a good clean I just wipe on some mop n glo works great in making the floor shiney