I live in Japan so my options should be bountiful, but I don't really know my choices because all I ever owned in the past was a giant tank of a single-sided composite-only player i picked up for $50 on ebay.
My first choice would be something cheap, so if it dies I can simply buy another one. The players I saw on Japanese auctions that I was most interested in went for around $300, but those were really top-of-the-line players and I have a feeling I'd be happy with something far cheaper that has s-video, a remote, and dual-sided play.
Other preferences would be good video quality, quiet, and reliable.
Why? I love the large-size art and box sets of laserdiscs and want to enjoy the ritual of opening them, enjoying the extras, and taking my time to watch each movie or episode as a special gift, at least until disc rot sets in.