I run astronomers.io on a 1GB RAM/30GB disk DigitalOcean droplet that costs $10/month. You can scale up the droplets, but it's not breaking a sweat considering how low volume the site is:
The mail is delivered through a free Mandrill account. The Discourse 30-minute install guide is well written and will get you a Discourse instance with minimal effort.
I know of two high-profile science collaborations that are just starting to use Discourse. The cool thing is that you can have varying degrees of openness. You can require users to be logged in to both read and write for example. You can also make the forum invite-only. In doing so, you have a perfect internal forum for your collaboration.
You can also mix public-and-private areas in the same forum. For example, on astronomers.io posts are by default anonymously readable. But in the Professors' Lounge subcategory, I've made it so that only logged-in users can read and write. Discourse also lets your set up groups (essentially by giving users tags) and you can give groups permissions for different categories.
The meta.discourse.org forum is really great for learning how to run Discourse since the formal documentation is still lacking.
So yes, I think Discourse might be well worth looking into for a science collaboration of any size.