[morzh]

Well,

a long solenoid inductance depends on:

1. Proportional to the Number of turns (square of it), so N^2
2. Proportional to the cross-section of the bobbin (considering wire diameter being very small relative to it), and
3. Inversely proportional to the Length of the winding.

So, you need to observe both geometry of the winding (the exact size of the cylinder formed by the cross-section and the length) and the number of turns.

The diameter of the wire is only important, if:

1. The gauge is too large and so the winding cannot fit in the same length as before.
2. Current rating of the wire is too small (it is not too large in the first place) so you need a larger gauge.
Note that the absolute DC resistance by itself is not very important, in most cases anyway.

The Litz (it is not the cloth insulation, but multiple strands forming the wire, every single strand being its own enameled insulated wire) vs solid is important at higher frequencies, but not necessarily very important: it will make the coil less lossy due to diminishing the skin-effect, but it might be not that much of a loss in the first place in tube radios. Resonant tanks are more sensitive to it as they need especially high Q-factor and could use lower losses, but again, most times solid wire will work fine.