You talk about an alpha and then beta - so assume in the alpha you're doing free testing for a very close set of customers, etc.
With that in mind - I'd price the beta, and of course it clear that it is a beta and that you're still working out the kinks. Then let customers self-select. Customers who expect a fully finished product won't pay for it - and in my experience, they won't like it *even* if you give it away for free.
On the other hand, customers with a real pain that your software solves will be happy to pay for it even if there are are few (non-fatal) glitches here and there. They're called early adopters for a reason. Also, early adopters tend to not be very price-sensitive.
At the end, what you want to learn, sooner rather than later: "is anyone willing to pay a real money for this?". Pricing the beta gets you there faster, in my opinion.
Now, beta customers would be taking a chance on you. So treat them well. Make sure you are responsive to any bugs/issues. Hand-hold them through the initial stages. And later on, when your product becomes a hit and raise prices, always grand-father these customers into their original plan.
You can always think of creative ways to offer more value for beta customers. For example, if you have two or three pricing plans, for beta purposes, you can make it a single price - and give the premium version at the lower cost. That'd be an incentive for them to sign-up now rather than later.
On this note - one thing I'd recommend avoiding - obscure pricing. I've written about this before:
If you're focused on SMB, then by all means, please don't be one of those SaaS companies that hide their pricing!
hope this helps.