Transporting as a transparent gif is easy, you just select the box, and you're good, but I can't get rid of that white ring around the outside.
Does this program support partial transparent pixels on every color? My image has a solid black outline, so there's a gradient from black to white shown in the color range, but I simply need partially transparent black pixels.
Most fixes cause the outline of the image to be very jagged and lack any sort of dithering or antialiasing.
You need to learn more about the GIF file format and the difference between 8-bit and 32-bit files, esp. in the way they can handle transparency.
To amend Nick's answer: Gif images only support 1-bit transparency. It is either on or off, with no in-between transparent values possible. And as such, when you export a semi-transparent pixel to Gif, the software must multiply that pixel with the background matte colour (which in most software can be selected during export).
The result is often a white aliased edge surrounding the graphic where the original semi-transparent anti-aliased pixels sat.
In short, it is a limitation of the Gif format. You will always have to live with aliased edges where the edges meet transparent areas in Gif.
The most acceptable solution is to switch to APNG (animated PNG) instead, which is supported in all major modern browsers, including Edge. APNG does support partial transparency.
Of course, with Adobe traditionally lagging behind the times, users can rely on AnimateCC not supporting output to APNG, and you will have to export your animation as a PNG sequence first, and then use a converter to save an APNG animation.
Some suggestions: http://littlesvr.ca/apng/
Support for APNG is now at almost 90% global:
Try this tutorial. https://www.youtube.com/watch?v=zTPcUgKCIec