Probably nigiri sushi is the most famous and most popular type of sushi in Japan and also outside of Japan.
History of nigiri sushi is relatively new than other types of sushi. It it told that nigiri sushi appeared in Edo (current Tokyo) in early 19th century. Nigiri sushi spread to nationwide in late 19th century due to introduction of ice maker and fridge using ice.
Nigiri sushi is usually counted and sold per piece. Most running sushi(conveyor belt sushi) restaurants offer 2 pieces per plate and the price is per plate but be aware when you visit sushi bar and sit in front of the counter. The price is mostly per piece even the plate comes with 2 pieces. If salmon nigiri sushi is JPY 300 per piece, the plate is JPY 600. Therefore if you do not have allergy or preferences, it is better to order a nigiri combo which comes with 8 - 12 pieces of different type of nigiri sushi. In case there is a type of fish which you can not eat, just tell the staff to change to alternative one. Usually the sushi chef will prepare within the price.