Use Handbrake, pick your quality settings for video etc. make sure you have it set to save in an .MP4 container, then got to the subtitles heading, and check the "Burned in" option at the subtitle track you want. Depending on your specs on your PC, you may want to encode in MPEG-4 rather than H.264 as that is a long process for low power machines.
Just an extra note, if you want to remux into MP4 from MKV, you will not be able to use the ASS styled subtitles, MP4 doesn't support these.