Not an expert on the subject
Then seriously read up! Not meaning to be rude, but considering that this question comes up every second day, there's plenty of info out there and in here. A simple forum search or Google could have answered this. The "pretty standard" settings in AE are uncompressed and that being so, bulky file sizes are normal. You need to use different Output settings and encode your files to compressed formats like H.264/ MP4 to significantly reduce file sizes.
I have looked things up thats why I'm here. Just cos I'm not an expert on the subject doesn't mean I have to do a university course on what "pretty standard" settings are. I'm only using after effects to render the videos and trust me, if I found something else to use, I would. I'm an audio guy not visual effects and/or file size master.
Forgot to talk about the last thing you said. I don't know where H.264/MP4 is but Ill find it.
we can't answer your question until you tell us what resolution, quality, compression, you need. editing, final output, coloring intermediate, keying, youtube upload, raw proxy, etc. the list goes on and on....
the list is broken into some off the top of my head
444 8 bit/10/12/16/32 per channel
compression-lossless "zip" compression, lossy jpeg, wavelet, delta interframed, intraframed
as in all things, you're gonna trade file size for cpu decompression/and or quality. that's also why the type of computer
you have determines if you need a proxy or not.
quicktime png 8 bit is math lossless, cineform wavelet is good intermediate editing, prores has many, many flavours of quality, as does dnxHD(youtube uploads). I'd read all their white papers. The bitrate will determine if your hard drive can handle them in realtime. So in actuality, time is money cuz you have to render proxies.
as a fun note, h.264 actually has a lossless setting of RF = 0 called main 10 profile