You could give mp4 a go.
The main determinants for file size with Export will be Duration, Frame Size and Compression (CODEC) used.
I agree that if you want a MOV-type format, the H.264 CODEC is a very good choice. Also, what Frame Size do you require? Setting this up in the Export settings to just what you need will minimize the file size as much as your chosen CODEC can compress.
Why not Flash?