The amount of liability insurance coverage that the state of New Jersey requires on an auto insurance policy is really low. They only require bodily injury of $15,00 per person, $30,000 per accident, and $5,000 in property damage. This is really an inadequate amount of liability coverage for anybody let alone someone that has a good amount of financial assets such as you likely have.
As for what is more adequate is really depends on your financial situation. For most people who own a home and have a good amount of money set aside a more reasonable amount of liability insurance is $100,000 per person for bodily injury, $300,000 per accident, and $50,000 in property damage. This would provide a lot more peace of mind than the minimum limit New Jersey requires.
If you have quite a bit of financial assets to protect you can also consider pumping your liability coverage to $250,000/$500,000/$100,000. The good news is that at most insurance companies it really doesn't cost that much more to increase your liability limits. The peace of mind that comes from doing so and protecting your assets in the event of a major accident is usually worth the cost.
You might even consider getting an umbrella policy. An umbrella policy sits on top of your other insurance policies, principally car and home, and provides additional liability coverage starting at $1,000,000. An umbrella policy requires higher liability limits on your car and home insurance policies which varies by insurance company but is usually either $100,000/$300,00/$50,000 or $250,000/$500,000/$100,000 on your auto policy.