I used Movers Not Shakers within Queens a few months ago. They quoted me a very low (IIRC, $50 less than the nearest quote) flat price for 3 guys and a truck. All the other places quoted by the hour with a minimum, some of them add +1 for transit time to and from the job. I had a very small amount of stuff, so I was pretty well under the minimums.
They were over 2 hours late the day of the move, and I think even later because they couldn't find the address, which admittedly was a small place on a one-way street. I had scheduled a locksmith, so I was not there for the packing. There were actually 4 guys, and they were reasonably friendly. The unloading was fast and efficient, and there was no damage.
I don't recall the mover search engine I used, it might have been linked from the USPS change-of-address site. You pick up to 8, and it emails your info to them so that they can call you back with a quote.