To recable or not to recable?

Honestly, I'd start with interconnects (similar to recabling) and maybe a CMoy or five (good general soldering practice). Unless you want your first run with an iron to be potentially at the expense of your nice Grados.

How to do a CMoy including schematics, part source options, tutorial videos, and in general lots of good documentation for the beginning audio electronics DIYer.

http://tangentsoft.net/audio/cmoy-tutorial/

Parts options include Mouser, Digi-Key, Futurlec, et cetera. Mouser tends to have cheaper shipping that Digi-Key, but Digi-Key often has parts that Mouser isn't carrying. Futurlec has some cheap bits here and there, but others are higher cost; inventory is not nearly as extensive as Mouser / Digi-Key, but includes some random bits like SOIC boards. Redco (among others) carries audio parts which may be hard to find on the above sites (e.g. Canare Star-Quad cable).

Soldering equipment: you can do through-hole more or less okay with any iron, even the cheap $10 POS versions in Radio Shack. But some adjustables e.g. from Hakko are not that expensive. You should start with some lead-based eutectic solder (lead is bad, blah, but it's easier and you're using small amounts and hopefully smart enough not to eat it). You should also absolutely have a multimeter of some sort, even if it's just a $10 POS special from the Radio Shack (or often, the home improvement section of the grocery store). Really, the cheap crappy multimeters are fine when you're getting started, but they can be a little trickier to operate (odds are it's not autoranging - you need to set the general order of magnitude that the measurement is expected to be in).

Best time to learn.

How to solder, Tangent's videos are good. Here's the link straight to that section.

http://tangentsoft.net/elec/movies/

The main thing is to pick up some cheap parts and start getting practice.

Yeah, the CMoy design is dirt cheap. Even less than that sometimes depending on the parts you get and from where.

A CMoy is effectively what you get if you tell an electronics student with fundamental knowledge of op-amps and how resistors and capacitors behave in AC circuits to make an amplifier in five minutes. It's dead simple. But it's also quite effective both as an entry-level amp and as a starter project.