An animated GIF becomes its first frame
A JPG holds one picture, so an animated GIF is saved as the first frame of the animation. If the frame you need is a later one, play the GIF and take a screenshot at the right moment, or use a video tool: Video to GIF works the other way round.
Transparent parts of a GIF are filled with white, or the colour you choose, because JPG cannot be see-through. Choose PNG to keep them.
Will it look better as JPG?
A GIF has at most 256 colours, so a photo saved as GIF often shows banding and dotted shading. Converting cannot add the missing colours, but the JPG is usually smaller and is accepted everywhere a still picture is expected. For a logo or drawing with flat colour, PNG keeps the edges sharper than JPG.