Sporty car that won't make insurance rates rise too much?

I'm a 18 year old male that is becoming to have an increasing interest in vehicles. After researching on several different "sport" cars (Subaru WRX/STI, Honda Civic, Subaru BRZ, Mazda Miata, etc.) that would give me fairly good gas mileage and reliability, I found a few that caught my eye. Those cars being the ones listed above, I asked my parents about selling my '03 Corolla that has been tinted, new hub caps, stereo system, horn, etc. For around $7,000 to put that towards a down payment to say one of the cars I was looking at. They told me that the insurance rates will surely rise being that I am a teenager, the cars I am looking at are faster than regular commuter cars, and are years newer than my current car. I want a vehicle that I would be able to modify as far as performance upgrades mostly, good gas mileage because I will need to be commuting to college soon, a good bit more power than my current car, and good reliability, oh and maybe not cost me an arm and a leg for insurance. I'm looking for a vehicle that I can feel proud of. Something that I can drive and know it is MY car. Doesn't need to be a speed demon. If you guys could give me some options as to what cars I could research more into, that would help me out extremely.

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