Winding coils is an art. You will make mistakes. Save the good stuff for when you know you've got it right.
Stranded wire has a larger cross-section, so you will need a larger coil. Stranded wire is for applications where the wire has to flex some (audio coils usually). Your mill coils should not need to flex, and solid wire is cheaper.
There is no "cheap" copper anymore, really. Radio Shack sells 'reclaimed' stranded wire, and their solid magnet wire may be reclaimed, too.
Since copper is expensive, it pays to buy the best coated high-temp wire you can afford and not buy it on a spool that was carelessly wound. I don't even see aluminum magnet wire sold to individuals, although it does have common industrial uses. Getting the connections oxide-free and crimped properly is hard to do. I don't like using aluminum wire except for high voltage transmission apps where weight is an issue.
You could use plastic coated phone/ethernet wire for practice winding. But it will not hold up under load because the vinyl insulation is not high temp.
