I have a background animation for a DJ set done in After Effects and it's one hour long. When I'm trying to export the video directly from AE I get an extremely big file (~60Gb).
Should I render my composition in Adobe Media Encoder instead? If so, what settings should I use?
For sure, I'm missing something so I'm asking for advice.
You can use any compression or transcoding application, Adobe Media Encoder is as good as any. You want to choose from among the presets, don't try to mess with the setting unless you know what you're doing. You want to use a media type that your DJ system will play easily, that might be an of several Quicktime or Windows media types. Look up the media file that your DJ software prefers or ask the manufacturer. You can probably get by with H.264.