PNG is the natural upgrade from GIF for still images: it is lossless like GIF, it keeps transparency, and it isn't limited to 256 colours, so editing the picture later won't band. This tool turns each GIF into a PNG pixel for pixel, with see-through areas left see-through.
For animations, choose "Every frame" to split the GIF into a numbered PNG sequence, one ZIP per GIF. Each frame is composited the way the animation plays, including frames that only redraw a small area, so the PNGs are full pictures you can drop into an editor, a sprite sheet or a video tool.
What to expect: a PNG of a GIF frame is usually somewhat larger than the GIF, because PNG stores every frame in full while GIF can reuse the previous one. Frame timing isn't kept, since PNGs are still images, and GIFs longer than 500 frames are cut at 500.