If you have expensive in car entertainment make sure your car insurance policy provides enough cover to meet the cost of replacing it and it has been declared on the application form, if it is not standard equipmenty in that car.
Even if you haven't had car insurance in your own name before you could save money, as some companies offer an introductory discount or may take an existing driving history into account. This may be applicable if you have previously driven on your spouses policy or parents.
Remember any claim made against your insurance company may affect your no claims discount and could lead to higher premiums. You can sometimes protect your no claims with an optional premium. make sure this is transferable to other companies though.