If it's progressive, you should be able to do a pixel width of 1. Unless I have good reason, I stick to 1.5 to 2 at the low end, depending on the project. I would just make a couple of quick test animations(create lines of 1,2,3, & 4 pixels wide), compress to all your deliverable formats and determine my min based on the most compressed file.
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.