The Fire Cavern is really again just a training ground for you to figure out movement and fighting. Choose around 20 minutes. When you find Ifrit, be sure you get Cure from him. The clock will stop once you defeat him, so don't worry about time to get back out. When you defeat him, you get Ifrit as a GF.

When you go back to the garden, be sure to visit the library and read everything you can find. Then take a nap :)

Final Fantasy VIII Walkthrough