Whenever you take your puppy outside of your home, he should be on a leash. As with collars, you can get overwhelmed with all the options available. For training, a straight six foot nylon or leather leash will do just fine.
Other types of leashes
If you are taking a casual walk, you may want to purchase a flexi leash as well. However, I would not recommend using one of those until your dog has learned to walk properly on a loose leash. As your dog gets older and better trained, you may consider purchasing a 20 foot leash for training purposes only. This will come in handy when training behaviors like come when called and distance stays.