Eh, you don't sound ready from what you have written
1) An SV650 imo is too much power for a new rider. I have one and its still intimidating at times even though I started on a much smaller bike ( a 250r). I couldnt imagine starting on the sv650....i mean its just as fast as an r6 up until the top end and well past the legal speeds
2) 3 accidents in 3 years? That is not promising
3)Cheaper? not really. The gear is a pretty penny, the tires dont last near as long (around 4k-5k miles before replacing) and the mileage of a sv650 is not that much better than a car. Not to mention, the insurance I have on my bike is on par with my car's insurance (35 a month'ish) and i am 25 with a clean driving record (no tickets or accidents since 15)
4) Safety doesnt mean squat if other drivers are yapping on a cell phone or something. Even if it's their fault, who pays the price? you would. Motorcycles never win
5) A new rider SHOULD never be going 2 up. Horrible idea. I don't and never want to. If I crashed, I could never forgive myself for taking another with me
You sound as if you are trying to justify getting a bike....which i can relate to. If you do, fore sure take a MSF course, Best 200 you will ever spend
QFT
I have no problem with a teenager getting a motorcycle since I've seen some that are great riders. But based on what you've said, you should NOT get a motorcycle. Motorcycles are money pit, if you want cheap, get a used Honda Civic.
And 3 accidents? If you already have 3 accidents in a car, be prepared to be in a lot more on a motorcycle. Especially when your accidents were from you not paying attention. There are a lot more things that you will need to pay attention to when you ride that you don't need to in a car such as gravel, potholes, oil, other drivers not seeing you and turning on to you (and trust me they won't see you), lane positioning etc. You'll have to ride so defensively and you'll need to always pay attention to what other people are doing if you want to stay alive on the road since on the bike, it doesn't even matter if it is your fault or their fault, the rider will always be the one who end up with the consequence.
If you are easily distracted, you'll always find more things to distract you no matter what you ride/drive. But this time if you rear end someone on a motorcycle, instead of just dealing with insurance company to get the car fixed, you might end up on a wheel chair for the rest of your life.
I hope most of the people that think it's a good idea for the OP to get a motorcycle doesn't ride or live in N.A. Riding in Europe is different since drivers there expects motorcycles. N.A. drivers don't and won't see you.