What's the best way to transport moving boxes across the U.S.?

About 20 packed and sealed moving boxes, averaging 20–30 lb. each, have to go from the Northeast to California. What’s the best and cheapest way to send them?

— Speed is not the most important consideration.
— Important factors are cost, reliability, and care in handling. Items are packed for protection, but they can’t just be bashed.
— Insurance must be available.
— The Northeast location is a small village with no services or amenities to speak of. It’s 20 miles to the nearest town big enough to have a Safeway and a Kmart.
— The California location is a major city.
— No other pieces (furniture, odd-size parcels, high-value items) are involved.

Do you have pertinent experience to help us choose a carrier or shipping method? UPS would cost a fortune.

U-Haul and similar self-transport options are not under consideration.