Hello there,
There are various little rules of thumb like, the inductance varies as the square of the turns ratio, but it's usually just better to have a formula or two.
For what you are talking about it sounds like you want to make air core coils and there are various formulas on the web for doing this. You basically decide how much inductance you want and then use the formula to figure out what a decent diameter would be and number turns as well as wire size. The number of turns affects the inductance and the wire diameter affects the current carrying ability of the coil. The choice of diameter is interesting, because for a given inductance i think there will be an optimum radius r where when using that radius you get the least resistance for a given inductance value (micro Henries).
Take a look on the web and see what you can find, and if you cant find anything i'll post a few formulas you can try. We can also try some optimization to see what radius works best for a given formula and coil shape.
For solid core coils (with some kind of metal or similar core rather than air) the procedure gets a little more involved, but most manufacturers these days provide the designer with a reference value for a given core usually known as AL. Knowing this value for a given core allows a little faster design to get the required characteristics you are looking for. A little trial and error and you can find a core with the right AL value for your purpose.
I do have to say though, that buying an inductor is much simpler than trying to wind one yourself. There are other things to consider too such as finishing varnish or whatever that make the coil more durable. This is true for solid core inductors, but for many air core inductors hobbyists usually wind their own unless they want especially high Q.
Just to get you started here is one formula for a multi layer air core cylindrical known as Wheeler's Formula:
I=0.8*(R^2*N^2)/(6*R+9*L+10*B)
where
R is the mean radius,
L is the length of the coil,
B is the build,
all above in inches, and
I is the inductance in micro Henries.
We could also solve the above for N and we get:
N=sqrt(5*(6*I*R+9*I*L+10*B*I))/(2*R)
and we could try to optimize for highest Q by calculating the total length of the wire and try to minimize that length while varying say R while keeping the inductance I the same. I think the optimum comes out when the length of the coil is the same as the diameter, or something like that.