What I like about Amazon is that they offer recommended videos. I go to something that I know that I liked in the past, then scroll through the recommended list. Not all of the recommended list is free with Prime, but they generally tell you when it is included with Prime on the face of the video. It's free with Prime when it has the Prime logo in the top left corner of the video.

Since I'm not yet subscribed, I also like that there's a free video as the first of the series to several of the series to check out whether I'd like it or not.

The first show of Avatar The Last Airbender is free to check out the player.

Looking at the recommended list of that, there's Legend of Korra, Astro Boy, Thunder Cats. Legion Superheroes, etc. Then if I click on one of those, there are more recommended videos.

I sometimes just scroll through that recommended list for fun, not even intending to watch the shows. Sometimes I go looking to see if they're on Hulu.

Edit: Also, there's also a Free with Prime link and a Free to watch link on the Amazon video front page.