My thoughts, because I like telling people what I think
Computer:
Yowser! You have 473 bucks budgeted for your PC. And it doesn't include a case.
Don't build one, for what you want to use this for - 80's classics and light web browsing - a beat up old P4 will do the trick. you can get one of those with XP for under 100 bucks.
I suggest you go XP for your build. It seems most BYOAC stuff is built with XP in mind, I am pretty sure its the most popular OS around here. You can probably get a CRT for free or cheaper if you look. Try a thrift store or craig's list. Nobody wants a 17 inch CRT. Your wifi stuff is also more expensive then yo ulist it. For the type of machine you are building I would put my budget at 250, max, and you can probably get one that will suit your needs for around 100 bucks.,
Also, lets think logistics, the whole cab is going to be 4 feet tall, that means the screen is going to be about 3 - 3 1/2 feet off the ground maybe? That won't be comfortable at all for an adult to use. I know the CP on my cabinet is like 34 inches off the ground, the CP is going to be what, like 25 inches? I would ditch the whole "second workstation" idea, unless your kid is going to be doing work on it.
Controls:
No need to get a mag stik, I have never used them, but from reading on the forums, it seems that they feel really different. I would just get a happs super or competition. A kid is going to use it, you want something tough and rugged, and those things are solid and around 10 bucks. If you want it for the switchable 4- 8 way, well, do you think it matters that much to the kid? Another option is a U-360, since it has built in support for 8 buttons, and you wouldn't have to buy an ipac, and you can map it 4 or 8 way.
Boom, I just saved you like 300 bucks buddy!