If you make a claim against the other party's insurance policy than you would not be responsible for a deductible. When making a claim under the Property Damage Liability policy of the at-fault party than a deductible is not due. If however you are making a claim under you own Collision coverage the deductible will be due. When making a claim under your Collision or Comprehensive coverage the deductible amount you chose at the inception of your policy is due whether you are at fault or not.
If you go through your own insurer but someone else is at fault than typically your insurance company will subrogate with that party for the monies they pay out for your claim. You then can ask your insurer if they will try to get back your deductible amount for you as part of their subrogation process.
When your car is totaled, the insurance company has an obligation to "make you whole," as that is defined in the policy. This essentially means you have to be left in approximately the same financial position you were in before the accident. The insurance company will typically write you a check for the actual cash value (ACV) of the vehicle, minus any deductible on your policy if you go through your own coverage.
If you will be getting a replacement car you can find out how much it would cost to insure here by getting a direct insurance quote.