I vote you build your own instead of buying...you come out cheaper in the end, regardless of what caliber you choose. Seriously, you'll end up buying a stock rifle and then want a new stock, rail, comp/brake/flash hider, grip, trigger guard, trigger, etc. You'll take a $550 AR-type stock rifle and end up dropping $700 on it in accessories over time and have parts leftover. Or build your own for around $800-$900 that'll be exactly what you want and out-shoot most rifles costing much more.
I built my latest one (bought my first one and built 3 now) last year using an Anderson upper and lower, Anderson BCG, Green Mountain 1:7 fluted barrel, slim Midwest Industries rail, Magpul stock, a Primary Arms 4-14x44 FFP Mil-dot scope and mount, and all the other misc parts for barely over $900 and the thing shoots better than some of these $1500+ RRAs, Larues, Daniel Defense, etc (handloads mind you). Watch for sales (Memorial Day is a great sale time) as it'll help a lot.
The caliber depends on your ranges to engage targets in my opinion. If you can keep it under 100 yards for your wife, then I'd go 223/556 for cost of ammo for other recreational activities with the gun. If you're thinking up to 200 then a 300 BLK would serve you well as hit harder, and the 6.8 SPC extending a little further to around 300 (sure people claim longer, just talking about good energy retention here).
Personally, I'd build a 223/556 first (that'll be alright to shoot some deer up close with and do other things with and save ammo costs), then save up for and get a dedicated 6.8 SPC upper and BCG to swap in later down the road. It'd be the best of both worlds, although trust me: I've tried using multiple uppers/calibers on one lower and I just end up wanting to buy another lower and have dedicated rifles hahaha
Good luck man and let us know what you decide