How to choose a moving company for a cross-country move

How do you know a moving company is legit and not out to rip you off? Even the ones with the correct licenses and permits have mixed reputations.

I will be moving from CA to the midwest this summer. I've been looking into "full service" moving companies to do the loading, shipping, and unloading for me. Unfortunately, every company I can find has some horror stories on the internet about extra fees/charges, items being damaged or lost/stolen, previously quoted prices being doubled, horrible customer service, etc. I'm beginning to get paranoid about paying someone money to put all my stuff on a truck and drive away with it.

I have a 1 bedroom apartment with what I think of as an average amount of stuff for two people. A company called ABF U-Pack Moving offers an intriguing option: they drop off a metal box(es) (6'x7'x8') at your place, you load/pack all your stuff, and they pick it up/ship it later. Storage is convenient because everything is already self-contained and easily warehouse-able. I like this option because I will definitely need storage at the other end of the move and I have the time to pack and load everything myself.

I guess I'm looking for either experiences with this type of service, or tips for not getting ripped off by a "full service" moving company.