There's no filesize difference between DXT5 and BC7. If you need an alpha channel, always use BC7 as it's higher quality.
If you don't need the alpha channel on a texture, consider DXT1 if you can deal with the extra quality loss. It's half as big as DXT5, but quality may suffer as a result.
Also keep in mind that crunch compression may reduce download size of your avatar, but it won't reduce VRAM usage. It also won't work on BC7 textures. It's a bandaid at best for avatars.