[morzh]

I do not have a fuse on my 20 radios, I might have it on one radio I restored for my dad.
At any event, I would rate a fuse at 1.5x the radio's max current rating, and make it a slo-blo (time-lag) type.
An inrush limiter, in my opinion, is an overkill for this type of application.
I used them in AC/DC switching supplies as there is a very sizeable inrush due to an unprotected discharged capacitance essentially in parallel (disregard the rect bridge) to the AC supply. In a radio with a transformer there is essentially an inductance (which is what an unloaded transformer is) and this does not result in a very strong inrush.
There is one possibility when a switch gets made exactly at the point of the AC voltage crossing zero, that could result in some DC-like behavior and saturation by the transformer, but not for a long time as there is some finite loss resistance there.

This said, the peace of mind is a priceless thing and if it makes you sleep better at nights, by all means the limiter is good.
The fuse is a good idea in any case.