Frankly, you sound like you've got it covered. For some applications you might want to use enameled wire so you can wrap it closely. And for VHF and UHF especially, coils will be much smaller.
Since you mentioned AM radio lets assume you are talking about MW and HF receive applications. See the links below.
For a receiver wire size can be small but different kinds of wire effect the capacitance between turns and so will impact the self resonant frequency. Also wire size impacts the "Q" factor.
For some kinds of applications, high Q is very desirable. Basically Q is sort of the inverse of lost energy.
The more conductive the metal is the better but the crucial region is the skin of the wire. So, the highest Q will be attained if the wire is silver plated. The wider the wire and also the wider the diameter of the coil the more inductance and Q, but because of the skin effect, tubing works as well (better by weight) than solid wire. Also, copper tape in a helical winding works really well.
There is also wire "litz wire" that uses multiple independent conductors, it has very good characteristics for RF coils at MW and low HF. It's kind of a woven wire.
Also - there are web pages where different kinds of wire (and insulated wire) are compared. Some kinds of insulation are really undesirable.
I have some (old) insulated solid wire that is not very good as RF inductors, its clearly because of the insulation because when I remove it it works fine.
Here, this is very very good:
http://www.g3ynh.info/zdocs/comps/part_1.htmlhttp://www.g3ynh.info/zdocs/comps/part_2.htmlAlso very very good
http://hamwaves.com/coils/en/http://www.g3ynh.info/zdocs/comps/index.html