Once the wort reaches approx 70 degrees F it's time to transfer into your primary fermentation vessel. It doesn't really matter what equipment you choose to use. There are pros and cons to everything out there. For your first few batches, stick with the plastic buckets from the original kit (if thats how you acquired your starter equipment) to make sure you enjoy home brewing before spending more money on more expensive carboys. Personally, I like the plastic 6 gal. Better Bottle carboys. Glass is nice but some of the injuries resulting from the thick broken glass can be pretty nasty.
Empty Better Bottle
Regardless of your choice, sterilization and cleanliness is extremely important for anything that comes in contact with the wort at this point. Using sterilized tubing, transfer the wort into your fermenter and aerate the wort. This can be accomplished many ways as well. Oxygen stones from aquarium stores, oxygen wands, or even just shaking or swirling the carboy vigorously can do it. **I would NOT recommend shaking or swirling a full GLASS carboy.** There are even videos on YouTube of people attaching devices to handheld electric drills to stir up and aerate their wort. If anything, it's good YouTube entertainment.
The next step is pitching the yeast. It is good practice to decant (pour off) the clear liquid on top of the yeast starter leaving the yeast cake behind. Like it was mentioned back in the yeast starter section, that starter liquid is great for yeast to grow and be happy, it is not great for flavor development. During your transfer it can be helpful to put a cup or two worth of wort into your flask with the yeast starter so it can be swirled around and loosen / break up the yeast cake. This makes pitching the yeast just a little easier.