Your team can host a static site (just HTML/CSS/JS, no PHP, etc.) on Github Pages. I've used it in the past with sites, and it's pretty straightforward if you know how to use Git, and not too hard to learn if you don't.
In terms of domains, I personally buy domains at Namecheap, you can get a .com for $10, but there are a lot of similarly priced options out there.
There are a lot of different hosts, with prices varying. To name a few: Namecheap, DigitalOcean, A Small Orange. I'd contact various hosting companies if I were you, they may be willing to discount the rates.
Feel free to PM me if you have any questions about websites or hosting, there's also a lot of info at the
webhosting subreddit.