David,
VLJ's (Very Light Jets) are coming and if you can capitalize around 2 million dollars to fund one, they might be right for you. With limited experience, the opportunity to fly one without owning it will be rare. In general aviation, insurance policies have a strong influence on who can operate the aircraft and those requirements are typically in excess of the FARs.
If you goal is to work for an airline, this board might be a good resource, otherwise check these links:
http://web.nbaa.org/public/news/pr/2...050210-006.php
http://groups.google.com/group/verylightjets