If you're just linking / embedding and not hosting the videos, then a simple notice, such as "We link / embed videos of others. We do not host these videos." would likely suffice.
However, if you allow others to post video links / embeds, then you should add a prominently visible "Report Video" button for people to use to flag video links / embeds, such as those, for example, that are sexually explicit.
If you intend to host user uploaded videos and are located in the U.S., then you should definitely register as an online service provider DMCA designated agent to fully take advantage of the safe harbor provisions of the DMCA.
U.S. Copyright Office - Online Service Providers
Registration cost has skyrocketed, since the last time I looked, to around $135. So it's not cheap, but it's, currently, a one-time fee.
In my view, writing (or copying from elsewhere) long-winded notices, disclaimers, user agreements, etc is likely a waste of time, and in some instances may increase your legal liability - yes, increase it!
Ie. having no stated privacy policy, in some instances, is legally safer than actually having one.
Consulting with an attorney is likely the best way to go, if and when your website becomes, or at the verge of becoming, very popular. At this point, in my view, don't sweat the small stuff - focus on growing your site first.
Ron