Animation Quicktime is NOT the way to go. This codec will only playback in real time reliably on a super computer. You need to pick a good distribution format that will stick around. PICK H.264. Read on...
If by large screen you mean a really big TV then make a standard HD 1920 X 1080 comp at 29.97 fps and render using the Adobe Meida Encoder. You can put your Animation Codec Quicktime in the AME if you like but I think there are better DI formats (Digital Intermediate). Pick h.264 as the format and pick the Vimeo or YouTube HD preset and jack the data rate up to 40 or even 50 and enable Multi Pass rendering. You will have a file that will playback smoothly on any modern system, even from a newer iPad or other tablet.
If you mean a 4K display then use the same technique but create your 4K composition using the standard 4K display size of 3640 X 2160 and use the YouTube 4K preset.
You can jack up the data rate for that preset also but don't go above 50.
This will give you a file that is technically as good or better than you would get with a fiber connection to a 4K broadcast. How the project looks when played back will depend on how good you are at choosing the right techniques for your animation and color grading taking into account the color space you're working in, the gamut of the display, and the motion of animated elements as it relates to frame rate. (Hint: that's why I said to choose 29.97 as the frame rate because animating illustrations and text to look good on a big screen is a lot more difficult at 24 fps than it is at 29.97 and you don't need 60fps because what you gain in the elimination of judder you loose in the addition of compression artifacts when the data rate is the same.)
One last piece of advice. Obsessing about the quality of your playback format to achieve the MAXIMUM result is for the most part a huge waste of time and energy. Get the color right and tell the story well and avoid juddering animations and you'll blow the audience away even at 10 or 12 Mbps HD. 90% of all quality issues in rendered animations that I've seen are issues of design and animation technique, not issues of rendering with the wrong settings.
Rick, thank you so much. I'm relatively new at this and have been making little pieces for web use so I wasn't sure how it will play out when it's shown on a larger screen. And to be honest, I won't know exactly how it will be shown until after a client meeting this afternoon. But I think I grasp most all of what you're saying and will put it to use. The only thing I'm wondering about is why Adobe Media Encoder? Can't I just render it out of the queue in After Effects using your suggestions? It's good to know, at least, I was going to start the project at a standard HD comp at 29.97, so at least I feel I stumbled on that correctly. But, man, thanks for your quick reply. It really helped.
The Adobe Media Encoder is encoding software and it does a better job than the Render Cue's output module. The output module is limited to rendering one frame at a time and all modern delivery codecs, especially h.264 benefit from a different kind of calculation.
BTW, Premiere Pro uses the AME exclusively for output. If you are not using Ray-traced rendering then any AE project can be added to the AME in exactly the same way you add a Premiere Pro sequence to the cue. One last point, choosing QuickTime h.264 as an option in the output module has always been a very bad idea because Apple does not really support h.264 rendering to QT and the output is buggy and lousy.