GHQ vs. "touched up" Axis and Allies minis

For me, there are 2 reasons for whatever scale you pick.
1. cost
2. fun
3. how playable are they.

Your call ... I wish you and your son many, many happy times saying "YOU SUNK MY BATTLESHIP!"

You should have a look in the Marketplace before you agonize over eBay prices. There is always someone who has a deal, or can relate to the tale of a 10-year-old inductee and will be flexible about prices.

Unless you want to use unpainted miniatures, I wouldn't buy shapeways

Who are the best sculptors for 1/1800 on shapeways? I'm fine with painting them. What kind of prep do they need before priming?

Another thing to consider especially with a 10yo is durability. The WaS models are plastic and hard to break even when using them a lot and throwing them in a bin for storage. Also the guns turn on many of the models. Kids love points of articulation.

The Shapeways WSF is not brittle at all. There is a lot to cover on the topic of "Shapeways." There are different modelers, different plastics, and different ways to prep and paint them. They have their pluses and minuses. I recommend you go to the Naval Modeling sub-forum and read some of the "sticky" references and ask about the options over there. One thing about Shapeways is there are now a lot more to choose from than GHQ. GHQ has very few subs, and a very limited assortment of aircraft. And the number of small ship classes (destroyers, mine sweepers, etc) and auxiliaries is covered by the Shapeways guys much better as well. GHQ would only be at parity with the capital ships. Also, a lot of the Shapeways are now available in multiple scales. If you don't see one in the scale you want you can send a PM to the modeler and request it. They are generally very open to helping a request.

My experience has been a little different.  I've had problems with GHQ superstructures and turret barrels.  I've got a Texas, Ranger, Langley, and a handful of aircraft and Thai ships in White, Strong & Flexible; I have yet to have an issue with pieces breaking.

I do put a little bit of foam in the tackle boxes for the Shapeways pieces, though.  They're not quite as durable as the A&A pieces.

Side Note:  I've only had one WaS piece break due to dropping.  I lost a secondary gun barrel off a Kongo when it hit a tile floor.