Thanks for the replies.
I have a late 2009 Mac, so no AirPlay capability, plus my Mac is on the other side of the house, so that wouldn't let me remote through the various clips.
I have a mid- 2009 MBP and use AirParrot to Airplay mirror my screen to my Apple TV all the time. It works well.
If you have an Intel Core 2 Duo or higher with at least 1 GB of RAM, it should work for you.
http://www.airsquirrels.com/airparrot/specs/
For moving through the various clips, you could use "Rowmote" or "Mobile Mouse Pro" apps on your iPhone / iPod Touch / iPad. These will allow you to move your mouse cursor on your mac remotely using your iDevice via wifi, as if you were sitting in front of the computer. I've used it plenty and it works well.
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In general, I have been hoping for years that Apple would come up with a good way to integrate Home Video into the iTunes / Apple TV world. After all, when you import your movies from your iPhone into iPhoto, those videos are immediately viewable on your Apple TV (albeit via the "Photos" section). But that is not the case for videos in your iMovie library, since they are typically not in the correct compressed format for iTunes/Apple TV to play them. Frankly Apple does not appear interested in solving this problem: When Airplay Mirroring first came out, watching iMovie library videos on the Apple TV was marketed by Apple as being a primary benefit, indicating to me that was their "solution".
OP: I'd advise you to pursue the AirParrot / Mobile Mouse Pro route. It is going to be the least amount of headache for you as you won't have to spend hours of your time or your machine's time pre-processing video clips. You can watch them all on your Apple TV tonight after only setting up Air Parrot and installing a mobile app.
That said, if you are intent on getting those videos into iTunes so that they are natively showing up on your Apple TV, it is going to require a lot of pre-processing on your part. You'd need to either:
1a. Use HandBrake like others are saying to transcode the videos into .m4v or .mov format. Then drag them into iTunes.
OR
1b. Use iMovie to "export" each video clip to iTunes, one by one.
OR
1c. Use iMovie to "export" each clip to iMovie Theater, one by one (until you run out of iCloud space in iMovie Theater and it starts nagging you to buy more space.)
1a and 1b will create a transcoded second copies of all those video clips, so now you are storing them twice (once in your iMovie library, once in your iTunes library). The .m4V videos ought to be smaller, I'd think.
Of course, the above will only get the clips into iTunes so they appear on your Apple TV natively. However without additional work you won't be able to tell one clip from another since they will probably all have non-sensical filenames. So you'd ideally want to add metadata. You can do that one-by-one inside iTunes by right-clicking on each movie file and selecting "get info".
Personally, I'd choose option 1b, above. This way you could title each clip in iMovie before exporting to iTunes. I'd use the following title scheme for each clip:
"YYYY_MM_DD Short Description"
So for example, in iMovie you come across a clip from New Years 2013. You title the clip, in iMovie:
"2013_01_01 New Years Party"
And then export that clip to iTunes.
This will result in your clips appearing in iTunes / Apple TV, and all will be ordered chronologically.
Another way to group them down a bit is to create "genres" for different years in iTunes. That is, once the clips are in iTunes, you can set them to "Media Type" = "Home Movies", which iTunes and Apple TV will respect, showing these videos only in the "Home Movies" category on Apple TV. (you should be able to select all the clips in iTunes at once, hit command-I for get info, and change them all to the Home Videos "media kind" at once. Shouldn't have to do it one at a time.)
Then, within that, you can take all the 2013 home movies in iTunes, select them, hit "get info", and put them into a "genre" called "2013 home movies". You can have other genres like "2014 home movies" etc.
The end result of this setup is that, when you sit on your couch and go into your Apple TV, you can just go to Computers --> Home Movies and then sort by genres, which will give you subcategories (2013 Home Movies, 2014 Home movies, etc.) so that you'll end up up at the lowest level with a list of clips from that year, ordered chronologically with a short description built into the title.