Q: What is the best way to determine which shipping company to use? Most of the aliya sites have listings for the East Coast. Also, are there any sites where new olim post how their delivery experiences went with their shipping companies?

A: You have asked the $64,000 question...
Picking the right company to handle your shipment is critical to getting your goods to their destination in good shape.
Of course, you should ask friends for recommendations. Their good (or not!) experiences can help you make a decision. In addition, I always suggest getting at least two bids for your move.
You should expect a representative to come to your home to perform a pre-move survey. This survey allows for an to estimate the volume of your
shipment so we can prepare a quote. Knowing your volume, may also lead to a recommendation for sharing a container (consolidation or groupage) or going with an exclusive container just for you. Based on this volume estimate you should be able to come pretty close to knowing your cost for your move.
Feel free to ask the surveyor about the volume of items you are not sure about bringing. This will help in your decision process about what you should or should not bring.
Your decision will be largely based on the impression you get from the surveyor, but you should try to look beyond that. Compare bottom line prices (and not just the per cubic foot or container cost) between the companies. Ask to go to a packing in your neighborhood. This will help you will get a feeling about the type of people who will pack your things and how professional they are.
Good sources of experiences and feedback about moves are the Tachlis forum, Nefesh b'Nefesh forum (only open to Nefesh participants), and the Jewish Agency web site.
There are good companies on the West Coast that specialize in moves to Israel, but now with the internet and easily available international phones, you can feel very comfortable considering a company in Israel as well, to handle your entire move. With an Israeli company handling your move, if there are any problems, someone locally will be responsible as opposed to someone who is 10,000 miles away.