Nobody can tell you anything without proper system info or other technical details like comp settings, render settings, specs and requirements of the screen and whatnot. Sorry, but "nice video" is useless and generic.
As Mylenium says, we need more information.
Some big questions would be:
What is the resolution of the screen you are sending video to? (Is it 1920x1080P full HD?)
How are you sending that video to the screen? (Laptop playing over DVI? Blu-ray player? Desktop computer using HDMI? Etc.)
What did you render before that looked pixelated? (Format, codec, bit rate, etc.)
- Use the the standard HDTV 1080 X 1920 29.97 fps preset for your composition.
- Add the comp to the Adobe Media Encoder
- Choose h.264 as the format option
- Pick the YouTube or Vimeo HD (1080) preset
- Render the MP4
Load the MP4 in your media player and select Full Screen
The resulting video will be as good or better than you get from HD broadcast cable or a BluRay disk.
If you are looking for 4K content let us know.
To learn about rendering and video formats please type "rendering" in the search help field at the top right corner of After Effects and study up. There is a lot to know about video formats and compression. If you are going to play with video you have to educate yourself.
You'll want to pay attention to the gents' comments above.
The size of the screen is pretty irrelevant. The playback device is crucial. Think about this: you can watch a movie on Blu-Ray on your computer. You can also project that same Blu-Ray movie on the side of a building. The Blu-Ray didn't change. The player may not have changed. The only big change was the size of the image.