Don’t rush to book with the company that gives you the lowest estimate. It'll be easy to discard high estimates but should you receive an estimate that is substantially lower than the others, inquire as to why.
When tipping the movers, it is best that you compensate each one separately to acknowledge the hard work by everyone involved in the relocation. More information on moving to nyc here.
In many cases, you can deduct some of your moving expenses from your taxes. For more information on how to deduct your moving expenses from your taxes please read Moving Guide -> Financial Issues
Basic Carrier Liability is a minimum coverage required by law. Under this option, the mover assumes liability for no more than 60 cents per pound per article, and this option is free. To learn more about Basic Carrier Liability read Moving Guide->Moving Insurance Tips