In my experience the best darts are steel tipped. The flight of a steel tipped dart often seems superior, and also the steel tips tend to grip the dart board better too. You will obviously pay a little more for the steel tipped variety but it is well worth doing so.
As regards to the weight of a dart, this is very much down to a particular players preference. The weight can vary hugely, with darts available as light as 18g right up to around 42g! As you can see this is quite a large weight difference, as some darts are twice as heavy as others. It is down to what you feel comfortable with as a player, there is no right or wrong weight. The great Eric Bristow, not a small man I am sure you will admit, used darts that weighed around 21g, which you really would not have expected. It is probably best to experiment with differently weighted ones and choose the ones that suit you best.
As regards the balance of a dart, the length affects the balance, where the weight is on the dart, so you need again to choose one where the balance feels right for your particular technique as a player. The shape of your arrow will affect your grip so make sure it feels comfortable in your hand. The shaft will be made of plastic or metal, and will affect the action of the flight. The length of the shaft will affect how your dart flies.
The flight is of the utmost importance, as it determines how your arrow flies through the air, and how quickly it flies. The flight helps to provide drag on the dart, so obviously the larger the flight the slower your dart will fly through the air. A larger flight will definitely provide more stability for your throwing. The most popular type of flights are the large kite shape or the teardrop, and they are the most popular for a reason, they are the best flights to use! I would change your flights as soon as they get a little torn or frayed, as they can certainly affect your game if a little damaged. The flights are relatively cheap anyway.
I hope this has given you some clues as to what will be the best darts for you, and will put you on your way to becoming a better darts player.