I stand to be corrected but I'm not aware of any basic video format that is interactive in it's own right. Is this for distribution? I use a multimedia authoring tool called AutoPlay Media Studio for this sort of thing.

On a DVD is several folders.
These folders will act just like a physical disc if you open/play them in the proper program. You do not need a DVD, and PD has several options for the menu/play structure. That may or may not be helpful. HP Envy Phoenix/4thGen i7-4770(4@3.4GHz~turbo>3.9)
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From a DVD perspective, I understand the idea of a menu structure as a mechanism to physically play chosen video clips that are stored on the DVD. When creating a menu structure for a DVD, what is handling the operation of the menus? Is that a software-based thing that "runs" on the DVD player or is it something simpler?

Although the implementation obviously has to be different for a file-based video production, the idea is basically the same. I have a set of video clips that constitute my video production. Now, I'm just hooking everything together in PD and creating a large (about 45 minute) video production of these clips with some "glue" to merge everything together. For this project, it would actually make more sense for the viewer to be able to select the clips they'd like to play instead of having to wade through the entire 45 minute production. There must be some type of multi-media scripting language that will allow you to build an operational menu structure and run the menu to allow users to make selections and view individual clips and come back to the main menu upon clip completion. This is such a basic operational need that there just has to be some type of application that will allow this to be easily built. I could develop this in a specialized programming language but I want something that can be easily distributed and doesn't require specific software to run it. Basically, I need something that will allow the grouping of a set of video clips (or possibly web links to where these clips exist (i.e. YouTube)) and provide the ability to setup a front-end menu system (with integrated video, images, & sound) that can be executed so the viewer gets a clean interface for interaction with the clips. Maybe it could be done in a Java applet that could run within a browser. Or maybe Flash? Other options/ideas? Appreciate any help.

Probably your simplest option would be to go for html. There are any number of free apps to do it with.

A while ago I would also have suggested 'flash' as an option but it seems to be almost dead in the water now.

If you go down the 'burn to folder' route you could distribute the folder set but you need to make sure that the host system has got a DVD player installed.

p.s. The software I mentioned has an option to build a standalone .exe that will run on any Windows system but I'm sure that goes for lots of other packages as well.

HTML and/or JavaScript is probably your best option for internet distribution. Java was a horrible internet language from the beginning and Flash, in my opinion, is more complicated and not very seamless. __________________________________
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