Is simple until the product isn't ready or is some marketing behind? Do they wait until they have a number of signups? Is there an optimal fixed duration?
This can be really useful for working out if you are missing key features, or for getting ideas for future direction of the product.
Maybe the best use of a beta/coming-soon page though is to try and get an idea of the market size. Pretty much the first thing I do when I have a new product idea is to slap up a basic signup page, and spend a bit of money on Adwords to get an idea of whether this is something people want or not.
This also lets you get a feel for how much customers will cost you to acquire (through Adwords at least) which can feed into your business/cash-flow planning.
It also allows you to get your page indexed and ranked by Google, meaning you'll have an easier time of it when you start trying to drive organic traffic to your site when you launch.
Launch as soon as user can experience the pitch message.
The time between these two is unknown and I guess would make sense not to set a concrete launch date. The sooner the user gets hands on it the better.
I'm not sure the referrals program is always the solution you want. You should try to make sure the people who are coming to your site are qualified, otherwise Joe will ask Alice, Bob, and Charlie to join. Those 3 won't stay for any meaningful amount of time (blowing 3 of your slots), and Joe now has upgrades/perks/???. It's more desirable for you to have those 3 users giving you input.
However, there could be a time when you don't want to limit invites, such as when you need user generated content. Then the more beta users you have, the more content you have generated when you go "live".