Handbrake is a transcoder, not a ripper. Handbrake always transcodes the video.
MakeMKV is a ripper. It copies the media from the disc to the hard drive in its original format.
“Best” is subjective, and depends on what you want to accomplish.
Many people rip the disc using MakeMKV, name the file correctly, and add it to Plex. The advantage is that the media is in its original format, with no loss of quality. Also, the process is relatively fast. Transcoding video is compute intensive and, depending on the CPU, can take quite some time. The disadvantage is larger file sizes and potential compatibility problems.
Others prefer to transcode the media with Handbrake or similar tools. This can help save storage space and reduce compatibility problems with older video/audio codecs (avoids transcoding by Plex Media Server). The disadvantage is the extra work required to transcode the media and possible quality reduction if the transcode is performed incorrectly (if you use the wrong settings, the resulting media may look/sound bad versus the original).
Suggest you try both methods. Rip a few discs with MakeMKV and load the output into Plex Media Server. Also transcode them with Handbrake and compare to the disc rip. Then choose whichever works best for you.
Plex has specific naming and organization requirements for movies, tv shows, and music.
Different media types must be kept in separate directory structures and in separate Plex libraries. No mixing allowed.
Follow the naming and organization requirements, especially with TV shows. The closer you stay to the documentation, the better your experience will be with Plex.