Do you need a media player to create digital signage on a screen?

Not necessarily. While media players offer a more powerful way to connect your screens, it is possible to connect to smart TVs which have system on chip (SoC), or internet cinnected tablets without a media player. However, if your screen has no direct internet access, then yes you will need a media player to connect.

I have a smart TV - should I use the inbuilt connectivity or add a media player for digital signage?

This depends on your usage. While commercial TVs with connectivity can be used, they aren't built for 24/7 streaming or intense data usage from multiple sources. If you're planning on running content all day, or you're streaming live data dashboards, video or other high intensity content then you should consider using a made for purpose media player.

I am displaying simple content such as a menu board or simple imagery for retail. Do I need a media player?

Not necessarily. Simple content such as menu boards or a few slides with simple images can be streamed relatively easily using integrated connections on your smart TV.