PNG or GIF?

I have absolutely no idea where to ask this question, so I've come here for help. I like to make sprites, but I've been saving all of them in the GIF format. It has come to my attention that PNG can also do transparencies and animations, but I can only save my animations in GIF anyway (I use Jasc Animation Shop). If this is all painfully obvious to you guys, I'll just say sorry in advance, but I've just had to learn as I go.

Anyway, I have tested both formats out, but the only difference seems to be file size. Which format is best for saving transparencies? I've tried to read up on the differences, but every single god damn article is in crazy nerd talk, so it tends to go over my head at times. I hope someone might respond here.

GIF blows. Just from my memory: PNG supports 16, 24, 32, 48 and probably more color depths, short palettes (when not all colours used), alpha channels, extra layers, colour profiles, offers much better compression, and is completely free and open. Use MNG for animation.

GIF sucks sure it supports animation, but it only supports 256 colours, it's full of legacy, and it's PATENTED, which means that it's PROPIETARY.