The minimum number of turns required for a 120 V, 60 Hz primary is a closely guarded secret. :-) Not really, but everyone always talks about turns ratios, but forgets to mention the minimum number of turns for the primary. Well, the iron/silicon/metal core of the transformer can accept only so much magnetic flux before it saturates and can't take more. If you go beyond this, the inductance drops a lot and you end up drawing a lot more current off the powerline and it will get really hot - not good.
A rule of thumb, for transformer laminations you may salvage from a junked 60 Hz transformer: Number of turns needed for the 120 V, 60 Hz primary = 800/(area of the core in square inches). You measure the height of the pile of laminations, and the width of the center leg of the E lamination. This width is measured along a line that would go vertical when looking at the E as the letter E appears here. In other words, imagine a single turn of wire tight on the center core, the area of the loop this single turn forms is the area. Do not include the outer legs of the E, or the I. A bigger area will make for a lower number of turns.
Once you have the number of primary turns, then you can do the turns ratio to get the number of turns for the secondary. Add a few more turns to make up for resistance of the wire voltage losses. If your powerline frequency is 50 Hz, you need 60/50 times the above result for your primary for 120 V, and twice that for 240 V.