Feel for you. Companies like Nrma generally have lifetime guarantees on repairs, only use new parts from Toyota dealership, won't pull metal out/straighten as it is deemed as weakened integrity but instead replace parts or undo the spot wields and replace the panel, they also have turn around times that they may not be able to meet based on part availability, there is big $$$z in that repair if done by brand standards.
Understanding that " you " are not at fault, you don't have insurance and relying on the other vehicles insurance company;
You need to prepare detailed information of the accident, this includes the situation, light level, your car being road worthy as in evidence of brake lights working etc. Don't assume they won't pull a technicality or they claim you to be at fault - it's what you can prove not always what happened.
Most importantly you need detailed information of your vehicle and any enhancements/maintenance to justify the condition of your vehicle. You need get evidence of vehicles for sale of a similar condition to present as the value of your vehicle. Then you have stronger merits to negotiate an agreeable "market" value of a mr2 that is different to red book. When they offer you a payout, they must gain your concent, you have the right to negotiate a fair amount based on current sale prices of vehicles plus/minus aspects based on condition.
Be aware some insurance companies do not recognise some kinds of accessories, upgraded rims etc. Get all accessories (that's everything the car did not come.p with when originally sold at the dealer) off the car prior to handing it in.
They will generally allow you to purchase the vehicle at a third of the payout amount depending on the vehicle impact/issues. Remembering your vehicle is now on a write off list so depending on the state may have extra expense to re-register.
Generally you will be offered a refund of your registration separate to the write off amount. This is very little money as it's only a refund on the registration fee component not the 3rd party or other fee components.
Should your vehicle be taken in for repairs or deemed as a write off however payment is weeks/month after, contact companies like "right to drive" who can organise you a loan car until sorted (subject to the other person admitting liability, insurance company accepting the claim, etc). Delays in payout can include the other driver not paying there excess, internal paperwork, furtger inspection of your vehicle upon them taking possession and all sorts of reasons, any drama, contact right to drive.
Hope that helps :)