I don't know of any that have a button called resume, then again don't think I ever saw one on DVD. The PS3 on most movies will stop and resume (when you press play) but not if you turn it off. My older Samsung does not.

For the disks (at least here) we can categorize them in 4 kinds

1) forced intro : intro before menu pops up and then you need to go to play, the intro could be previews but could also be something else
2) menu: menu pops up and you need to go to play to start the movie
3) previews: starts with preview and then continues with the show, the menu does not pop up, some are completely forced (can't FF or skip) others you can FF and others can be skipped one at a time. If you want the menu (for example for subtitles or audio selection) you need to press menu
4) movie: The movie start immediately (obviously there are the FBI and other warnings we have become accustomed to seeing). If you want the menu (for example for subtitles or audio selection) you need to press menu