[Kintsukuroi.]

Hey there.

I was in a similar situation a little while ago where my car was declared a write off but the damages were just over half of the worth of the car. The car was a 2015 so it wasn't like it was old but the cost of repairs was 26.5k of a determined value of 53k.
I hadn't been put on the insurance as the owner/primary because we get better rates if I am out on as a secondary driver. Plus, if I get into an accident, it won't count towards my premium.
However, my parents got the cheque because they paid for the car, they're on the insurance and technically they own it. Now, they took that money we got from the insurance and bought me a different vehicle but I didn't particularly get a say in which one I got because I wasn't buying it.

Now, I can't say how your situation would work because technically the car was registered under your grandmas name so technically she owns it despite you both being on the insurance. The fair thing to do would be to let you pick out a car with their help or spilt the cheque 50/50 with your grandma. Did you pay for part of the insurance? Because if you did, then you would be able to use that and mention that you paid for part/all of the insurance.

About the car that was declared a total loss. I personally wouldn't want a car that's been in an accident much less one that has been declared a total loss for safety reasons and issues with the car down the road. Plus, you don't know what hidden damages are there until it's too late.

Can you ask if they can get a mechanic to check it it over? To make sure there's nothing dangerously wrong and so you have an idea what may need replacing. Plus, get it checked to make sure there is no underlying frame damage or engine issues.
You also want to make sure that the car wasn't titled as being "salvage" or "non repairable" because that can lead to troubles insuring it. Check out the DMV for more specific information regarding your state.

I know where I am for example, if a car is declared as DPO (parts only) you can not use it or register it and it remains like that on the cars registration. However, if it's declared as salvaged, you can insure it to use it but it has to go through a variety of tests, repairs and inspections in order to be marked as a rebuilt car (and will stay like that on the papers) and that still can affect insurance premiums.