I applied many times over the years. I made it to the second round twice, before finally making it all the way with my newer movie.
There are three labs - the writers lab in January, the directors lab in June and then the Producing Lab in the summer. For writer/directors, the usual trajectory is to go to the writing lab. Then you may be invited to the directing lab (they also invite a few new projects that hadn't been to the lab). The producing lab is separate, and just for producers - it's both a lab and a yearlong fellowship.
An important distinction to make is that Sundance doesn't help you raise money. There ARE grants that the institute gives out every year, but they're separate from the labs. What can happen, however, is that you might get introduced to people who can help you find money. But Sundance does a great job of focusing on the creative aspects of the process. Even the producing fellowship is called the Creative Producing Fellowship. The whole focus is more about trying to tell the best stories possible.
For my film, my producers applied to the producing labs first, and got in. I have no doubt that helped me to grease the wheels with my script getting in after that, although I still had to go through the same rigorous application / interview process. By the time I went to the labs, the ball was already rolling on the movie (we'd already been working on raising money, etc). And by the time the directing labs appeared on the horizon, we were already in pre-production, so I wasn't able to go to those.