As usual first thing is to make a backup.
2nd thing is to make a backup
3rd thing is to make a backup.
Do you get it?
So, then go to components->joomlacomment->content settings and make sure that complete uninstall is set to 0 (no).
Save it and then you can uninstall joomlacomment - the comments should be left untouched. Install the new version. Make sure to read the readme file first, and this should be everything.
About the mod_comments - well if you use it - you should install it.
com_mmsblog is part of the package, so you don't need to do anything.
If anything goes wrong you can write here or just revert to your backup and try upgrading again.