buying AE86 questions

i want to buy a AE86 for a first car and i was wondering...

my parents say that any 2 door car is classed as a sports car by insurance and therefore costs more is this true?
if it is true does the hatchback 86 cost more or isn't it classed as a sports car because its a 3 door.

also what exactly is it called. i call it a Toyota sprinter AE86. but ive also heard it called corolla, so what do i ask for when im looking?

You're not going to find one in decent condition for under $5000. Get a cheap, safe FF car for your first car; at least get something that has airbags. Sorry, but your Initial D drifting dreams will have to wait until later in life.