Then it seems your task is straightforward. Since all three cameras (3200-5200-7100) have the same sensor resolution, it comes down to what features you cannot live without, or whether or not a particular body is suitably comfortable or rugged.
If sensor resolution is not a deal-breaking issue, you could make an argument for a less expensive set of choices: 3100-5100-7000, which are IIRC in the 16 Mpixel family.
I just steered my nephew toward a used 3100, which is about as dirt-cheap a way as possible to get a really nice DSLR to learn with. Beats the socks off my ten-year old D100.
I don't know how the 3100-3200 series cameras stand up in practice, but my D100 and N80 cameras withstood a ton of outdoors abuse: heat, sand, dust, humidity, rain, clanking around on my hip while scrambling over rocks, ice, brush, etc. I'm sure someone on this site can testify to how much they have abused a 3100 or 3200.