I built one with some friends as a final project for Engineering Physics II. Keep in mind that a key goal is to match the resonant frequencies between the primary coil and the secondary coil. The resonant frequency of the secondary coil is based off of the size of the toroid. To tune the frequencies between the primary and secondary coils, we attached a moveable tap along the primary coil, wired the tap to the transformer, calculated the resonant frequency of the secondary coil, and then calculated the placement of the tap based on the resonant frequency of the secondary coil.
As a side note, a 1 watt transformer is barely going to give you anything. Our transformer had a power output of 270 watts (we used a neon sign transformer). Our arcs measured from 12" to 24". We verified this by putting a ladder close to the tesla coil, measuring the distance between the two objects, and then verifying that the arcs struck the ladder. The maximum length of your arcs can be estimated by taking the square root of the wattage and multiplying that number by 1.7. Basically, if everything in your apparatus was absolutely perfect, you might get a 1.7 inch arc.
Check out these websites if you are serious about building a Tesla Coil. Make SURE that your calculations are correct!! These things are really (let me emphasize REALLY) fun, but if you get hit with a streamer, that might be the end.
http://deepfriedneon.com/tesla_guide.htmlhttp://www.deepfriedneon.com/tesla_frame6.htmlFeel free to message me if you want some more info, it really was an awesome project.