The fit is one of the most important things for long term use of the bike. In my opinion 300-400 dollars spent on a Giant or Specialized or other quality brand that offers good value at the lower price point is well worth it. Plus if you go to a good local bike shop you can look at different kinds of bikes like, hybrids, comfort bikes or a mountain bike and you can test ride them. If you are serious about your wife riding with you it would be smart. Also, don't underestimate that extra 5-10 pounds that the cheaper bike will weigh. And if your wife ends up wanting a better bike you end up spending more anyway. If she never rides it you can sell it for more than 25 dollars on the used market. Which is about all that a department bike will fetch.

A good bike you might sale used for 50% of new value if in good condition but you'd be lucky to get 25% value for a department store bike in the same condition.