HKer, If you haven't already completed basic training, leave the 'lil woman at home. You wouldn't have anytime time to see her, even if you were allowed.
As far as quarters or billets, thats a roll of the dice. If you get post housing or live on the economy (read: off post housing)the size can vary. You could end up in a shoe box or a palace, depending on what is available. It was my experience growing up in a military household (and my family had decent housing since dad was a O-6) that post housing was nice, but you were subject to inspections, to make sure you weren't punching holes in walls, painting the place black inside and the house had to be spotless when you moved out. On post housing is not guaranteed, you might end up staying in the visitors quarters (a military run motel)or a regular motel/hotel for a while.
Pets were allowed (at least in officer billets), but there were size and number limits. Again a subject addressed by the housing office that places you.
E-3 pay isn't all that much, probably better than when I was in ( I enlsited after high school). I always lived in the barracks. Also some posts have very limited family housing, and you may be required to live on the economy. If that happens you would probably get "separate rations" for meals and a Varibale Housing Allowance (VHA)which help, but it's not that much once you start spending the money.
The spousal employment issue is also a roll of the dice. Your wife could get a job in the exchanges or on the economy again, or she could apply for a Govt job in an office. It all depends on whats available, her skills, etc, just like here.
I had a friend who was an E-6 (SSG) and his wife worked in a bank while they were stationed in Bremmerhaven Germany. They lived on the economy and rented a nice house with their two kids at the time (1988). I visited them after I got out of the Army in 1987. They even had a family dog. When they PCS'ed from Virginia in late 1987, he went over first and arranged the house for the family to avoid many of the headaches of not having a place to move the wife and kids into right away. The wife and kids followed about 2-3 months later. I would suggest you consider the same, just so you know your wife has a place to stay, even if she moves back home for a short time stays with her parents or other family.
As far as your MOS stuff, I'm at a loss. I was a MP, and know nothing of that secret squirel stuff.