If these are vob subs in the .sub + .idx form, it doesn't matter whether it's mkv or mp4, those are just container formats, both can hold subtitles.
If you're having problems with colors, try converting the vob subs to .srt. It's easier to deal with .srt, but either should work. An .srt file is plain text, there's no way to get the colors screwed up because that's all controlled by the playback application. I've never had problems putting either type into .mp4 files with Handbrake.
As far as subtitles go, "forced" has nothing to do with what you want. Subs are either "soft" or "burned in".
"Burned in" makes them part of the actual video stream, they can't be removed later or turned off, nor can you reposition them or change colors, etc. They are "hard-coded".
"Soft" means they are in a separate "stream", a sub section of the container file. The playback application controls position, colors, font, etc. If you have a subtitle stream and set it to "default", this means it will automatically be on when the video plays. If it's not set as default, you won't see the subs until you turn them on manually.