YouTube shows three popular videos from each playlist and it lets you restrict the results to a certain category, like Education, Music or Sports.
Creating a playlist is easy and, by default, each playlist is public and can be embedded in a web page. Instead of posting 3 or 4 related YouTube videos, create a playlist and use the code provided by YouTube to add it to your web page: you'll include a single player and the visitors will only need to click on the "play" button once.