You are new! Welcome to the camcorder forum.
I have a HX9V, similar to your HX30V. I have a "smart" Sony 55" TV, so know nothing about your Samsung.
What works best for me is the previous model to a Western Digital WD TV Live Streaming Media Player
It takes nearly any video file on nearly any media, including an external HD, and sends it to an HDMI port on my TV. It comes with a remote and useful menu structure. It has a long list of other features that I ignore.
My process starts with using the software that came with the camera to copy my clips to my computer and catalog them. In your case I think it is called "PlayMemories". I can also use that software to join or edit clips creating new files of equal quality to the origninal. Or, I might use a third party editor with more creative control, but the output will not be equal to the 1080p60 .m2ts files. I then use Windows to copy the files to a USB powered HDD that I plug into the media player. I can send the file from my computer to the HDD on WiFi, but it is slower. I end up with a convienent way to watch what I want and a backup of video files I think are important.
There are other ways to do it. Some TVs and BD players will accept USB devices such as external HDDs, thumb drives and SD card readers but results seem to be mixed. Some BD players will read the original format .m2ts files copied on to standard DVD data disks. The Sony PlayMemories software will create a version of disk called "AVCHD Disk" on a standard DVD. And, there is always the option of buying a Blu-Ray burner.