Had the same problem with mushy rice when I moved from Asia to the UK for uni and had to buy "british-style" long grain rice from Tesco and other supermarkets. Fixed it by washing the rice a LOT - like up to 10 times until the water was actually clear.
(Back home we wash rice only 2 times and all the surface starch is washed off. My theory is that rice I ate at home is vacuum packed while the other rice bags aren't, so maybe the grains rub together more during transit and result in more small starch dust??)
Also don't worry about the water cup measurements, just do it the Asian way: Fill pot evenly with rice, put tip of index finger on the surface of the rice layer and fill with water to the first knuckle of your finger.
How to proceed to make basic east Asian style plain white rice:
Maybe I'm biased cos I'm Asian and have eaten plain rice every day of my life but if the rice is cooked properly and is nice and fluffy, I won't need to add any extra seasoning, even sesame oil.