I'm enchanting a longsword to have a really strong fire damage effect, and I want it to be "Cast on Strike", but when I cycle through my options, it's not there. I'm using a Common Soul Gem, with a Flame Atriarch soul. Do I need to use a better soul gem?

What am I doing wrong?

I assume you mean the enchantment effect is not there? That must be because you dont have any spells that cause fire damage. Just buy a simple fire spell and you can enchant anything you like with that effect.