Handbrake is a nice tool for transcoding video. One great thing is that it has a lot of options. One bad thing is that it has a lot of options. 
Here’s a very, very quick guide to using Handbrake. It should handle the majority of standard Blu-ray and DVD movies. Is this “the best” for your situation? Most assuredly not. “Perfect” Handbrake settings don’t exist. However, this will get you started and you’ll get a feel for things as you work with it. You’ll eventually settle on a group of settings that work best for you.
Transcode one or two movies, see how they work, then adjust as necessary. As transcoding an entire movie can take some time (hours), you may wish to transcode just one or two chapters as a test. If things are to your satisfaction, then convert the entire movie.
The end result of this will be another MKV file. Why? You mentioned subtitles. MKV is the most flexible container (file type). It supports all major subtitle types, including VOBSUB (DVD), PGS (Blu-ray), and SRT (text). The MP4 container only supports text subtitles. If your subtitles are all in text format or will be burned into the video, then feel free to use the MP4 container.
Also, this is for 1080p or lower video resolutions. It would probably work fine with 4K, non-HDR video. I’ve no experience with Handbrake & 4K, so cannot say for sure what the results might be.
Also note that discussing Handbrake settings is somewhat like discussion religion or politics. Some people are very passionate about what is right or wrong. Others are more agnostic. With respect to what is below, I’ll just say that this should work for most things and adjust as necessary. If you need to tweak something, then do so. If you try and it doesn’t work, then put it back. Experimentation is good and making mistakes is how people learn.
Tools: Make sure you have the current versions of each.
MakeMKV - rips movie from DVD/Blu-ray to your system.
MediaInfo - provides useful information about your media.
Handbrake - transcodes video & audio to other formats
Step 1. Rip the disc with MakeMKV, if you have not yet done so.
Step 2. Analyze the MKV file with MediaInfo. Keep the window open. Text view preferred.
Step 3. Launch Handbrake. Process movie.
Step 4. Add to Plex library. See how it works.
Note: Suggest you create a test library of type “Other Videos” to begin with. Use it to compare multiple versions as you experiment & tweak things. This will keep Plex from trying to load metadata, etc for the movies. It will also keep Plex from getting confused as to why there are so many different copies of the same movie. Once you find one you like, move it to a regular Movies library and delete the others.
Handbrake
A) Load the MKV file into Handbrake.
B) Choose either the HQ1080p30
or SuperHQ1080p30
preset. Don’t worry if your video is not 1080p, Handbrake will adjust accordingly. The HQ preset will run faster than the SuperHQ preset. However, the resulting output file will be larger. Try both. See which one you like best & go with it.
C) Adjust tab settings as follows:
Note: If you do choose MP4, then check Web Optimized
.
Framerate: Set to same as shown by MediaInfo.
Quality: Constant Quality, 20 for Blu-ray discs, 18 for DVDs.
Encoder Preset: Slow (HQ default) or Very Slow (SuperHQ default).
First audio track: AAC 2.0, match source bitrate (see MediaInfo), but 320kbps max.
Second audio track: If source audio is AC3, then choose AC3 Passthru. If another format, choose the AC3 codec and match source bitrate/channels, up to 5.1 channels, up to 640kbps.
The above are the audio formats compatible with the widest variety of Plex clients.
You may find other other formats, such as dts, dts-HD MA, EAC3, and TrueHD (+ Atmos), on your discs. Feel free to experiment with those as well. If your clients support those audio formats, choose the appropriate passthrough codec in Handbrake. It will copy the audio track unaltered to the output file.
Select the desired subtitle track, if any, to be copied to the output file. Uncheck Forced Only
and Burn In
.
If you have an external SRT subtitle file, use the Import SRT
button to add those subtitles to the output.
There are many possibilities for subtitles. The above will copy the desired tracks to the output file. Experiment & read to learn about other options.
Note: Forced subtitles are generally used for translation when actors are speaking another language. For example, in Avatar when the characters speak Na’vi and the translation appears on-screen. If you know the subtitles are forced, then you may wish to burn them into the video. This will make them part of the video track. They cannot be disabled as they no longer exist as a subtitle track.
- Chapters: Rename to match disc if desired.