@Mike Heth Since you can't buy VA as anything but an individual, you basically list the income from your rental and it's share of the expenses on Schedule E and file it all on a 1040 at the end of the year. Sounds complicated, but HR Block or Quickbooks will handle it easy enough (possibly Quicken) so no need to rush off hiring a CPA right off the bat. Spend it on the mortgage and repairs, but make sure you set aside money for maintenance and other hiccups (1994 means you're likely looking at an almost 30 year roof and with appliances having a life of 7 years normally, some of them could be coming up for replacement as well). Sock away as much cash as you can that is left over from the rental as well as your quarters allowance and after a year, you could buy another 4 plex OO with a low down FHA loan - or refinance this one to free up your VA and do it all over again - provided your wife is willing to move that quickly with a 3 year old).
Buying in IL doesn't automatically change your HOR so you'll need to discuss your situation with your base housing office to see if it would be beneficial for you to change it or leave it as whatever State you currently claim. Also keep in mind that as long as you are active duty, some of the capital gains rules won't apply for the whole 2 out of 5 years owner occupied exemption.
And don't get too caught up in the formulas on here - they are valid and pretty solid to go by - but you're looking at getting into an income producting property with zero down, fixed rate, low interest financing for 30 years and Uncle Sam is going to give you a nice tax free check every month to pay for your quarters while in reality your neighbor is buying your property for you. Your out of pocket $200 a month for a place to live plus utilities which is less than the other unit generates in depreciation per month (can't claim it on your side until it's rented out to someone else). The other expenses you simply divide in half for a duplex and deduct that half from your rental income - half the lawn mowing, half the snow plowing. Half the property tax bill. More than half the insurance policy (your agent can give you a breakdown on that one since your policy needs to cover you and your belongings as a homeowner as well as the property next to you as a landlord). Finance in your funding fee and negotiate the seller to pay all your closing costs (money is cheap now - $3,000 in lower sales price but you pay that much out of pocket for closing fees isn't worth it - the difference in the payment is $15/month and it's deductible.) I used to own a real estate office in an Air Force town for almost 10 years - we listed the houses and showed the seller what they would net if they paid all closing cost vs someone negotiating that much off the price. Same bottom line to them. For the buyer, they had to come up with about $500 out of pocket total.
So, how did you determine that you are getting the property that much off of market value? If that's an accurate valuation, then there are some problems with the property or repairs that need to be made that you maybe haven't found yet. Why is the seller volunteering to leave almost 10% on the table? Seriously, that's as likely as him handing you a $20K check the first time he meets you - gonna have to do some more digging to figure out why.