Talk to an insurance sales agent. Lose the term "full coverage" as it is meaningless, IMHO.
Your main concern should be liability should you be at fault in an accident. You also want to be sure that you are adequately covered as to under and uninsured operators. AZ may limit that amount to your liabiity coverage.
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In your case, the coverage should be about protecting you and not necessarily your car. The more liability the coverage you have the more you're protected from personal liability. If you're at fault in an accident, you're personally liable for whatever your insurance doesn't cover. I never advise getting the basic minimal coverage, especially if you have assets.
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Damage to your car is covered by collision/comprehensive coverage. When you own a low value car, you may decide that collision/comprehensive coverage is more expensive than is justified by the risk you are insuring against (damage to your car). The decision on collision/comprehensive coverage and the deductible amount is simply a cost v. benefit analysis. However, the more important issue is making sure you are covered for the damage/injuries you cause to others (liability coverage) and for the damage/injuries others cause to you (uninsured/underinsured/medical payments coverage). Make sure you talk with an insurance agent about what coverage limits are appropriate for your financial status.
Disclaimer - We have not created an attorney/client relationship. Please do not consider this legal advice addressing your specific case.