I am wondering if all of the specs need to be matched or are there some that don't need to be exact.
It completely depends on the application. Unfortunately you don't give us enough information to provide you with a good answer. However, in general stepper motors are fairly standardized. If you get one with the same step size, and the same general shape and size, and you can wire it up correctly (since the driver uses 4 wires it's pretty easy to convert a 6 or 8 wire to 4 wire use) then you should be fine.
If the device that uses the stepper is using it near its limits in terms of speed, torque, etc then you may have problems if you don't match the winding impedance, mechanical resonance, etc. This is only a problem in high performance machines, though.
I would contact the manufacturer, if possible, and get their recommendation. If not, try a different motor out and see if it works. Chances are good it'll be fine.
The step size is independent of the wiring - a four wire stepper at 0.9 degrees per step is the same as a 6 wire and 8 wire, just the coils have taps in them (or separated). So you will need to match the step size regardless of the wiring.
basically the limiting factors are the physical properties of copper,
it's bulk resistivity, thermal conductivity, and tensile streength.
make the wire too thin and it'll snap, or be so long that you'll need an impractically high voltage to achieve the desired field,
make he wire too fat and you need too much current..
more turns of thinner wire don't otherwise get you a stronger magnetic field for less input because the thinner wire has a higher resistance so you end up burning the same amount of energy in the field winding either way.
Best Answer
For highest efficiency and lowest loss you normally want the resistance to be as low as possible. So you start with the number of turns or length of wire required to produce the desired motor performance, then choose the largest diameter wire that will fit. If you don't know how many turns are required then just put on as many as possible and test the motor on a low voltage. Then adjust the number of turns depending on how much more or less speed/torque you want.
You can calculate the number of wires that fit in a particular area using basic trigonometry, but in practice you will probably need more space due to insulation thickness, uneven winding patterns etc. The insulation on thin wire is a larger proportion of the total area, and the wires are difficult to wind evenly without overlapping. Thick wire may be hard to bend and get in the right position for best packing.
A bobbin is easier to wind and assemble, but wastes space that could be used for windings. Therefore the resistance will be higher, leading to greater loss and more heating - and a plastic bobbin will melt if it gets too hot...