Interesting thread. Are we talking about the "What is this ham radio thing?" crowd, that s wanting a CCR, to dip a toe in the water, or more serious than that? How much more seriously is that person wanting to get involved?
Early stages of neophyte:
$5 DMM (Harbor Freight, etc)
Some decent hand tools. (Pawn shop, estate sale, etc)
Moving on from there:
Temperature controlled soldering station.
Power & VSWR meters (frequency appropriate)
Higher quality DMM
Analog VOM, if getting involved with tube/valve equipment.
Cabling tools (PowerPole, coaxial, Mole, etc)
That is just a starting point, and to be coupled with instruction on using said equipment properly.
I don't know if the temperature controlled soldering station is absolutely necessary... Sometimes, at least in my case, it was better to use a single tool for everything, and get really good at it.
Even in high reliability soldering courses, we didn't use temperature controlled stations (although I don't even know if they were available when I took them).
Of course a person could MAKE a lot of test equipment, that would be an adventure in and of itself, or even just make an accessory kit for a SWR analyzer ( a step attenuator would be nice ).
I think the ideal way to go would be to use a club that hopefully has test equipment to figure out what is wanted to begin with.