When I was looking at getting into this business I called Landstar because I had heard good things about them. At the time they were requiring so much OTR experience and they weren't taking any more vans. They apparently have limits about how many of each vehicle type they lease on. It probably couldn't hurt to call them though. It was a while back when I talked to them.
The downside, and this is what I've heard from other folks who lease on to them, is that starting out it's kind of difficult because they don't have dispatchers in the traditional sense. You work with their different agents to get loads. It's more of an independent sort of setup. That's what other folks have told me, so it would probably be best to talk to someone who drives for them to get the straight scoop.