You can use domain-based email (email@example.com), as well as other great Google services by applying for a free Google Apps for Nonprofits account. Google offers verfied 501(c)3 nonprofits free Google Apps accounts. Normally, you would pay $5/month per email address or $50/year, so this is a great value.
You can find more info here, but the short story is that you will need to complete an application process, then setup Google Apps (verify your domain, and then set up accounts). Verifying your domain can be a little tricky if you are tech-challenged, but Google offers several ways to do this.
Google does not ask for your IRS 501(c)3 letter, but instead asks for your EIN (IRS Employer Identification Number). The snag for most local faith communities is that their EIN may not be in the IRS database of charitable organizations, even though they have a letter as a 501(c)3. Most local congregations are however, covered under a group EIN from their denominational body—as long as the “deductability status” of that organization in the database is “Group”, which extends to subordinate units. Obviously, you shouldn’t use the denomination’s EIN for paying employees or filing taxes, but this seems to be the best way to work within the Google Apps for Nonprofits system.
Google Apps offers a really great tool for migrating all the emails from your old email hosting over into Google Apps. Contacts and calendars can be exported and imported in. In addition to email, calendars & contacts, Google Apps includes Google Drive (for sharing/collaborating on documents & spreadsheets), and many other tools.