Self-host might be a good option, or youtube or vimeo. Or even Twitter. But Instagram is a wierd choice.
Probably not twitter, any remotely popular link shows 'sorry we can't show this, maybe try reloading' for users without an account, unless they're very persistent.
Meta: this had gotten much better in late January, but is back to where it was again.
Yeah, I can't see the instagram thing despite being logged in.