A good game dreidel needs to be able to be stuffed in a pocket - so something between one and two inches tall/wide/diameter is about right.
Assuming we want to spin the dreidel with one hand as is traditional, a game dreidel can't be too heavy. A good target is 0.3 to 0.4 oz (10 grams) based on a quick survey of the wood and plastic dreidels in my house. Note that the weight of the dreidel in combination with the shape and spinning tip affects how long the dreidel spins.
It turns out that many dreidels are weighted. This doesn't translate into unfair advantages when playing basic dreidel - however, it affects the game play. If, for example, most spins result in a nun then the game gets really boring. The solution is to have a precision fabricated dreidel. In addition, a smooth and regular spinning tip and a shape that allows for a clear fall can minimize the affect of fabrication imperfections.
The point where the top touches the ground is the spinning tip. A sharper tip typically means that the top will spin longer. If the tip is made from a relatively soft material like wood, however, a sharper tip is more fragile - if its dented the dreidel can't spin evenly. Many non-dreidel spinning tops are created with a sharp metal spinning tip for this reason. Most dreidels however have a more rounded tip - and most inexpensive dreidels have a tip of the same material as the top body.
As mentioned above, the body shape needs to be balanced for fair spinning. The shape of the body also affects the spinning difficulty, the duration of the spin and the dynamics of the dreidel landing. The location of the center of gravity in relationship to the overall height of the dreidel affects stability of the dreidel. Center of gravity is also affected by the width of the dreidel and the distribution of the weight in relationship to the spinning axis. The bottom line with regard to the shape of a basic game dreidel is that it should be forgiving of a slow spin or an off center spin.
The body shape also has a very functional constraint: a good game dreidel must clearly display the result of the spin. This rules out rounded shapes where a dreidel can come to a stop in between letters. Four and only four possible landing positions are a must.
Also known as the shaft or stem of the dreidel, the handle is typically cylindrical. Some times shaft has decorative flourishes but as long as the cross section is semetrical around the axis, spinning shouldn't be affected. For example, driedels with a small ball at the top or with an "X" cross section are generally easy to spin as long as they roll easily across one's finger tips when they are being spun.
Keep in mind that the thicker the diameter of the handle, the harder it is to squeeze, particularly for small fingers. Also, a thinner diameter handel can typically be spun faster because the spinner gets more TPF (turns per flick). I settled on a 3/8" or 1/4" diameter handle and it seems to work well.
The length of the handle needs to be long enough to let ones fingers grip the shaft, but not too long that the dreidel is unstable and the spinner can't maintain the spinning access. Tops can be design for one handed spinning or two handed spinning which requires a longer shaft. Because a long thin handle would be harder to fit in a pocket - and a dreidel is traditionally a one handed top I recommend sticking with a handle of about 1/2".
Consider not only the pocket stuffing requirement but also the frequent falls off the dining room table and the occasional sneaker crushing on the hard wood floor. Obviously a steel dreidel comes to mind - but my recommendation here - for the sake of both the dreidel and the floor - is a solid plastic dreidel. Wood and various metals also do well depending on the shape and construction.
In addition to strength, the choice of materials also affects manufacturing cost, fabrication precision, and weight of the dreidel. A blown glass dreidel can never be precisely made - for better of for worse the shape will always have one of a kind imperfections that will likely affect the spin. The material also will affect the quality of the fall, causing a plop, a klunk, or an extended bounce across the floor and under the radiator.
I always assumed that a longer spin is a better spin. Think about this though - dreidel is a pretty boring game to begin with and who wants to spend more time just watching the dreidel spin and spin and spin and spin. I recommend that a game dreidel spin elegantly about 5 seconds - but no longer.
Does all this sound daunting? Yeah - buying one of those plastic dreidels doesn't sound half bad anymore...