How do I know which notch size to choose?

There are multiple sizes of v-shaped notched trowels and square notched trowels. These sizes are: 4mm, 6mm, 8mm, 10mm, 12mm and 20mm. In order to select the correct trowel size, you should select the trowel where the mm measurement roughly equals the inches of tile you fit, plus 2 inches. For example,a 6mm trowel would fit a 6-8 inch tile.

Do I need a trowel with notches, what are the notches for?

The notches do two important things. First, they make it easy to apply only a specific amount of mortar. No matter how much mortar you pile onto the trowel, the notches apply it in nice, even lines of identical thickness. Second, the trowel creates spaces between the lines of mortar. These allow air to escape when the tile is pressed into the mortar. Without the spaces, you could get air pockets that prevent the tile from lying flat or adhering properly.