To randomly "pick" images for individual frames, you will need to go through some really tedious work to set it up. Ready?
For each of your 100 images, make them ALL 1 frame long. Afterwards, distribute them all in time so that they don't overlap. If you're using a 30fps project at the default 10 seconds, that's 300 frames. You can go through the list of images and move the playhead forward 1 frame with the Right Arrow key, then type the 'i' key to set the image's in point. To make the task slightly easier, select the bottom most image in the group and starting with the playhead on frame 0, type the "up arrow" key (to select the next image *up* the layers list), type the "right arrow" key (to move the playhead forward one frame) then the 'i' key to set an in point for that layer. Repeat the "↑, →, i" sequence until finished.
The next thing you want to do is select the Group containing the images. Check to make sure that the time length of the group is the same length as all the images combined in the group (100 frames.) If the timing is correct, Clone the group (type the 'k' key).
You said you tried making an Emitter and weren't satisfied with the result, but I'm going to recommend you stay with the Emitter. It's probably the best/easiest option to use.
For the Emitter Source, use the Clone layer you created. Set the Shape to Rectangle and the Arrangement to Random Fill.
Set the Width/Height of the Size parameter to your project size.
For a similar project I did, I set the Emission Angle to 270º (which is a "straight down" direction — not that there should be any movement, but "ya never know" ;)
Set the Birth Rate to 0 and the Birth Rate Randomness to ... say... 100 (to start — more later).
Initial number 0.
I'll cover Life later — but set it to 0.1 to start, for now.
Set Life Randomness, Speed, Speed Randomness to 0.
For variation, you'll want to set the Angle Randomness to 360 or something greater.
That's the basics.
Turn OFF Play Frames and select Random Start Frame. [Every time you click the Random Seed, you will change up the order and variation of the playback.]
Key parameters for variation:
Life and Birth Rate Randomness. Life is how long the image will appear in Playback. Birth Rate Randomness will be how many different hair images will be displayed per single frame in playback.
The Life parameter you choose will be determined by the Frame Rate of your project. Life, regardless of project Frame Rate is in Seconds. If you set Life in a 30fps project to 1/30 (0.03333333333333 [use all 14 digits!]), the emitted object will appear for exactly 1 frame. If ALL your projects in Final Cut Pro are 30fps, then this will work as created. You may find this is not exactly what you want, so the best option is to make this parameter available to be able to adjust "to taste" — up to 3 or 4 frames in playback makes the image more noticeable and it's nearly impossible to tell it's more than just a frame or two.
Birth Rate Randomness will provide from 0 to x-number of Clone layer frames in one frame of playback.
The best way to set up both of these parameters is with a Rig > Slider so you can set minimum and maximum values.
Right click on the Emitter's Life parameter and Add To Rig — Create new Rig — Add to New Slider.
For the minimum Slider value, set the Life to 0.02. For the maximum Slider value, set the Life to... I went with 0.15 (however, my project setting was 60fps, so you might want to go with half of those value — but try them out to be sure!!)
Right click on the Birth Rate Randomness and Add to Rig — Rig — Add to New Slider. At the minimum Slider value, set 0. At the maximum Slider value, set 1000 (again, try this out — if you're in a 30fps, try 500).
You will want these controls available in Final Cut since templates applied to projects in FCP tend to be "conformed".
But wait, there's more!
I don't recommend using a Generator template. In Final Cut, if you expand the Generator longer in the storyline, everything slows down and if you make it shorter, everything speeds up unless you using Timing markers like Project Loop End. I recommend creating an Effect for Final Cut. If you need to use it like a generator, then use an Adjustment Layer and apply the effect to that. You also have the extra benefit of being able to make Effects Presets of the instances you apply (saving the parameter settings you apply).
I know this was probably a lot to take in. Hope it helps!