After Effects is not to great with GIFs so the best way to work with gif is to: a) prepare everything in AE b) export that animation as a video (f. eg. h264 mp4 or any format that you need. If you need something with transparency - remember to chose codec/format that supports that) c) open Photoshop d) import ypour video into PS e) export your gif by going to File/Export/Save for web
As for file size everything depends on: a) what FPS your animation have (lower fps = smaler size b) file resolution - smaller resoluion - smaller size. I know that it is obvious for most but if is not to good on compression side so standard full hd animation saved as a gif can give much larger file size than some standard video formats.