I want to use Premiere Pro to create small sized (300kb or less) GIFs. The typical set up would be a static image that doesn't move, and then an animated part (from a video) inside the static image. What would be the best way to accomplish this without going over the size budget?
First. Premiere is not the best tool to make a small size gif. Premiere is a video editor. You need a compositor.
Regarding a program, I use Hit Film which is free, and I also use Blender for 2D animation, (also free). If you want, you can use After Effects.
When using Blender you need to use emission as the shader.
Second. You need to plan your palette. This is probably the most important thing to reduce file size while maintaining a good quality.
The flat style is very good for an animated gif, and this is actually what revived the format. Use flat style and do not dither the image.
Export your animation-sequence as still PNG and assemble and export on another program, for example, Gimp.
File > Export > Media. In the new window, under "Format" select "Animated GIF"
You'll then have to play with the quality to get 300kb or less. The size depends on the length and how many unique colours you have in your video. Premiere isn't really the best place to make animated GIFs, but it works.
A compositor like "Adobe After Effects" is good Choice for creating GIFs, First Export Your Animation in Looseness AVI or MOV format from Premier Pro, so there will be no degradation of quality, if you want your GIF to be transparent, export your media with Alpha Channel for that Refer this article.
1) You can also export as JPEG sequence and then Merge those photos in Photoshop to create GIF, Refer this tutorial from Adobe.
2) You can use Adobe After Effects Plugin Called GIFGUN, take exported loosless/alpha channel video in After effects and this plugin do it's work, there is few options that will bring your GIF size under 300 kb, or else if GIF size is bigger then you can Compress it Online with tools like Online GIF optimizer.