We are interested in a fresh start for our organization with a new website using CiviCRM and Drupal. However, we're not sure if we should wait for the CiviCRM integration with Drupal 8 since it's the most recent version of Drupal, or start our full build in Drupal 7. Any feedback is welcome.
The short answer is easy, which you can take away from Does CiviCRM work with Drupal 8 and how can I help? — CiviCRM is not yet fully functional with Drupal 8. You can see issues tagged for Drupal 8 in JIRA, and even better, help test and develop the Drupal 8 branch code.
The long answer is more complicated, and depends on your organization's development timetable, technology cycle, technical resources, use of Drupal for other purposes than hosting CiviCRM, first-adopter culture or lack thereof, and like factors.
First of all, Drupal 7 is not going away any time soon. It will continue to be supported until three months after the release of Drupal 9, which is not anticipated until 2020 or 2021 at the earliest. The large installed base of Drupal 6 prompted vendors to develop a long-term support mechanism. Considering that Drupal 8 is by any account a much bigger change from 7 than 7 was from 6, and that 7 has an even wider installed base than 6 did, one may reasonably expect that there will be demand for a Drupal 7 LTS version as well.
Now, if your organization already has plans in motion to end your own use of Drupal 7, getting support to launch a new D7 project may be hard. In that case, you might be better-off waiting for CiviCRM 5 and full Drupal 8 support later in the year. On the other hand, if your organization will support D7 for the forseeable future, launching on D7 with an eye to updating to D8 in a few years may make sense. Or, if you are new to Drupal altogether, and you have technical expertise in Symfony, Twig, and other D8 technologies, you may be better off skipping D7 for now, and having to re-learn all that's changed for D8 in the near future.
Most of my clients on CiviCRM do not have dedicated IT resources, and rely on our company to handle maintenance and updates. These clients we are keeping on D7 for now, and will probably not migrate them to D8 for at least another year, until the future of modules like Webform are more certain. We are also keeping an eye on the Backdrop CMS project, a fork of Drupal 7. There is a request for Backdrop support in JIRA, but as there is not much demand for the product (yet?), movement is slow.
And finally, if your organization does not or will not use Drupal for any other purposes other than to house CiviCRM, you might weigh whether WordPress should be considered.
I am working with an organization that has been struggling with that question. They were originally planning to upgrade their Drupal 6 site to D8, but D8 progress has been so slow (notably lack of webform module & incomplete CiviCRM integration) that they have decided to switch to Backdrop. Backdrop-CiviCRM integration is functionally complete, as is the Webform module. They are sponsoring work to port the Webform-CiviCRM integration module, which will complete their needs.
Much depends on your timeframes and ability/willingness to help address the issues referenced there. It would be great if your org can help push forward the Drupal 8 work.