The oversimplified difference between the 3200-5200-7100, all of which have 24 Mpixel DX sensors, is that you get a LITTLE more of everything as you move up the line: a little better AF module (11 vs 39 vs 51 AF points), a little better viewfinder (pentaprism vs. pentamirror, better viewfinder magnification and coverage, etc.), a little more in the way of dials and hardware vs. menu adjustments, better weather sealing, etc. etc.
Many of the features on the more expensive versions may or may not be that important compared to the extra cost.
A D3200 has all the basics you need to control composition and exposure (P, S, A, M modes, exposure compensation, a variety of metering options). It even has a lot of the in-camera nifty tools like active D-lighting, AUTO ISO with adjustable upper limits, Picture Controls, etc.
It's easy enough to compare features and specifications. Unless you absolutely need some feature that only the D5200 or D7100 offers, and don't object to the size of the D3200, the lower cost model may be enough to gain access to a 24 Mpixel DX body. If money is no object, get the D7100 and get everything there is to get in this series. If you can deal with less, the 3200 and 5200 offer alternative price points.