In the last 16 months I bought used bikes off Craigslist for the entire family (3 bikes) and averaged about $400 each for solid do-anything-that-I-need-them-to-do bikes that saw 2400, 1100, and 90 miles of travel last year with no mechanical issues (the 90-miler was bought in November). These bikes will last for years to come with normal maintenance and repairs that I learned to do off youtube and bikeforums.com. That is about the same price as $1300 transmission job on my car during the same period. Note that if you plan to use the bikes for commuting (dark mornings and/or evenings) or to haul things (groceries, typical errands), you will also need items like lights and <<insert desired rack/pannier/backpack/trailer gear here>>. You might also need additional clothing if you plan to start riding while it's still cool in the mornings/evenings. Depending on your actual use and handiness or lack thereof, you can almost spend the purchase price of a bike cost just outfitting your two bikes to do these tasks, so keep that in mind.
Regarding new or used--some folks are voracious readers and love to consume the details about every task they attempt (like me). Those folks can do a pretty good job at nailing a good purchase the first time, new or used. Others prefer to learn by talking or working with other folks. Buying new through a bike shop or used via a community workshop offers valuable knowledge and experience provided you're not just talking to a clueless teenager. Only you know which camp fits your learning style--and it is true that bike fit is important for consistent riding.
In spite of how much biking has helped me financially and physically, your situation is slightly different. (1) You only spend $150-160/month driving a guzzler which means that you're not driving many miles/month, and your savings/month will be much lower than mine were. (2) You're deploying in June, so you could spend a bit of your cash on bikes only to have them sit for months, especially if your SO doesn't ride as much when you're not around, or your next location is less convenient for bike commuting/errands than you prefer. (3) You and/or your wife might find that you don't like to ride before temps are at the shirt-sleeves and shorts temps, which would also mean little riding for the next couple of months leading up to your deployment.
So this is really a gut check on you and your wife's goals rather than on the finances of the matter. If it were me, I would buy the bikes and ride the wheels off until June and see how the deployment plays out (whether I liked it or not---I bought them, so I'm riding them!), or I would throw the money at the debts and keep a mustachian eye on my other finances. You can always revisit this option later this year when you know more about your deployment (and your debts will be completely gone by then, I'm sure).