My recommendation is absolutely to have the child in an FAA approved child restraint seat (assuming the child is under 40 pounds). This should be the forward facing type. If the child is over 40 pounds, he/she may use the lap belt.

Booster seats are banned by the FAA from use during taxi/takeoff/landing though they are allowed for the cruise portion of the flight. They do not offer the same level of protection as a hard shell safety seat. The seat should be placed in a window location, never between other passengers and the aisle.

I think the suggestion of allowing the child to play on the floor is a dangerous one. Clear air turbulence does happen, particularly on transpacific flights and it does kill and injfure people. A child playing on the floor during such an incident could hit the aircraft cieling before you could do anything about it. And, of course, if there were an actual crash, it would be physically impossible to restrain a child seated on your lap.

I know that these are hihgly unlikely occurences, but considering there is essentially no cost difference, I don't see any reason to risk it. Think how much more comfortable you will be knowing that your child is safely restrained in his/her own seat.