Hosting Videos vs. Embedded Videos vs.

In the process of building a website that will allow members to upload or embed short videos of themselves. Lots of talk about never host videos yourself, or people uploading inappropriate content to your site, and all kinds of things.

What would be a good process or solution to let a user upload a video to the site and prevent the upload of inappropriate material? youtube api?

I would like my site to operate much like the simplicity in uploading a video to facebook, or embedding a video to facebook. Thanks in advance!