Favorite time period? Hmm, I'd have to say in the generality of that question, it would have to be the Cambrian period. The lands were pristine and virgin, volcanism was shaping the super-continent, the sea was teeming with many new creatures, some of the first recognizable ancestors of us terrestrials. Heck, even my favorite little creatures, the trilobites, are just dominating the seas. It was born from an apocalypse and will die to one as well, but during that short period of calm, life was everywhere and it had adapted many of the things we take for granted today, like our spines.
What a time to be alive, not like now where we're at the start of a mass extinction event. But at the start of the genesis for the biodiversity all around us, no matter how common or exotic it is.
It's not the first life that sprung out of the geothermal pools, it's not the first time life left the seas, but it's one of the most important time periods for life on Earth. If I could, I'd just stand at that primordial sea in my life support suit and cry because it's just so beautiful and inspirational to me. Who knows, perhaps I would even see the first molds clinging to the rocks on that long distant shore, hundreds of millions of years ago.