It's important to know what kind of pet carrier is going to be sufficient for the cause - what it is being used for. Pet carriers are great for short outings, crate training or if you plan to train your puppy to sleep in one at night.
There are a lot of really cute "fashion" pet carriers on the market today...the cloth, vinyl or thin plastic types we've seen in a variety of styles. However when purchasing one, again keep in mind it's primary use. They need to be safe and able to secure your puppy so he/she can't fall or jump out, large enough for them to lie down comfortably and have ample airflow. Many styles have the little snap inside to "attach" you pet BUT use extreme caution and common sense if you choose to do so. Never leave your pet unattended in one as proper supervision is always the key.
Pet carriers (crate style - also known as pet taxis) are great to use when traveling, especially in the car since you can secure the crate with a seatbelt and leave the safe driving - safe! Early proper training can benefit both you and your pet but it is never to late to start at any age.