This is actually a really good question that I’d be happy to answer. It took me a while to figure out how to save good quality GIFs that weren’t over 1MB.
I’ll start with a GIF I made about a year ago. I wasn’t originally able to post it directly as a picture post because it was too large. For it to post (and move!) it has to be, like I mentioned above, around 1MB and around 700px on the longest side.
This one is 1.2MB, 1000px x 721px, and 64 colors.
How I would save it now would be with Lossy 14. Lossy is the last option on the second column.
Now, the GIF is 865KB, 700px x 505px, and 256 colors. All that at 149 frames!
The thing that makes GIFs large is when a pixel has to change its color, at least from what I can tell. Lossy will keep some pixels the same color longer in order to save on size. There isn’t a big difference visually from 1 and 14 Lossy.
The only issue you may run into is it may leave trails you don’t want. This is a big issue for my origami GIFs, for example. Lossy would tend to leave pixels where a fold had occured, and it just wasn’t a good look.
I don’t even know if you can tell, but pay attention to the burgendy background when a piece is folded away. It leaves some pixel residue. This GIF is around 300KB.
The final one was then around 800KB because I passed on the Lossy. I also use a limited palette (shoutout to colourlovers.com!), which saves a lot of space.
Also, one closing thing that is the bane of my existance: Browsers have no color management. Like with a printer, you have to set the color manage properly to have all your colors print the same as you saw them in Photoshop, but browsers don’t have this. The best you can do is make sure your proof setup is Monitor RGB (View > Proof Setup > Monitor RGB). The GIFs look different from Firefox to Safari on my Mac. You can’t really do anything about that, but if you find your colors aren’t saving properly, it might just be a browser display issue.
I hope that helps!