Stick with Term Insurance
With the exception of a few situations (supporting a special-needs child or sibling; for estate tax purposes), the only kind you need is term. As the name implies, you buy a policy for a set period—anything from a year to 20 or more. Should you die during that time, your beneficiary gets the death benefit on your policy. If your goal is to protect children, choose a term policy that will give you coverage until your youngest is 23 or so; by that time, kids can support themselves.
Shop Around Online
Check out term insurance rates on reputable websites such as selectquote.com and accuquote.com.
Buy a Generous Policy
Specifically, you require one with a death benefit that equals 20 times your loved one's annual needs. I know that sounds like a lot, but if a child or parent requires $50,000 a year for living expenses, that works out to a policy with a $1 million death benefit. I suggest replacing 20 times their annual expenses so that your survivors can invest the money conservatively and live off the interest rather than eat into the principal. The amazing thing is that a 20-year, $1 million policy for a 40-year-old woman in good health can cost just $850 or so a year, or less than $75 a month. Make sure your policy is guaranteed renewable: As long as you pay on time, it can't be canceled.
Never Make a Minor Your Beneficiary
No life insurance company will write a check to a juvenile. If you name your child as the beneficiary, he and his guardian will end up in court, where a judge will become the overseer of the money. Avoid that by setting up a living revocable trust and making the trust, not a person, the beneficiary. Whomever you have appointed as the trustee will be able to use the funds to take care of your child according to the directives you've laid out.