It would be hard to go wrong with 22 AWG wire for nearly everything in your radio that carries AC or DC power (filaments, B+ bus). For lower-power signals like connections to IF transformers and audio stages, 24 AWG would be fine. Teflon-insulated wire is superb but may be hard to find; PVC insulated wire is an acceptable alternative, although be aware that its insulation can melt and also will combust if it gets hot enough.
You can use solid copper wire for all point-to-point connections where no flexing takes place - it is a little easier to work with than stranded wire. For flex connections such as the pendant cables that connect to a magic eye tube or speaker, it is necessary to use stranded wire.