It is becoming more common for research funders and grants to stipulate that research publications must be made available Open Access. Typically, this is done by applying a Creative Commons license to the research publication. It is important to be familiar with your funding terms to confirm which Creative Commons licenses will meet your Open Access requirements, and to ensure that your intended publisher uses Creative Commons licenses. More liberal licenses (such as CC BY or CC BY-SA) will often meet Open Access requirements.
Data is also frequently deposited under a Creative Commons license. Data is not copyright protectable, per se, but using a Creative Commons license helps provide notice to the user about how the data may be reused. Creative Commons licenses can also provide a good reminder that attribution is required for any data reuse. The most liberal licenses (such as CC0 Public Domain Dedication or the CC BY license) are often viewed as the most compatible with data deposits.
Under some funding or grant requirements you may find there are both data deposit and Open Access publication requirements. It is important to ensure that any Creative Commons license you use will be compatible with both your data and publication obligations.