Hate the stop and go

I watch my videos on YouTube and Vimeo and occasionally they will pause and stop again. I put up with this for years, but a friend gave us a new, big TV, 65", and suddenly those pauses are really irritating. What am I doing wrong? Anything I can do to fix old videos? What should I do for new videos to prevent this? I thought it was Comcast, but when we house-pet sit I see the same thing on my laptop and their tv. The more I see it the more frustrating it gets. Thank you, Rick