Nikon d3100, d3200, or d5100?
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D3200 is the one I like the most ( the one I have )
My grandparents have the d5100, and I like that one too, but I like D3200 the best. And d3100, no one in my family has so I'm sorry I can't say anything about it.
But, I think Nikon D3200
I use this tool to compare cameras.
http://snapsort.com/...om/compare
Me? I'd probably get the Nikon D5200, unless I could afford the Nikon D7100.
Among those I would chose the D5100 for having best features like ISO control in third stop increments, and for having the least noisy sensor.
Canon t3i with magic lantern
The low resolution LCD on the D3100 will soon annoy you and both of the others have better image quality and a lot lower noise at high ISO.
Between the D3200 and D5100 I would go for the D5100 - which I explained in detail to somebody else earlier here
If you are planning on doing any sports-action photography, realize that the D5xxx series - most likely due to the optimization of the articulated LCD screen has a poor shutter delay.
The D3100's shutter delay is: 0.200 sec in AF-C (sports continuous mode)
The D3200's shutter delay is: 0.163 sec in AF-C (sports continuous mode)
The D5200's shutter delay is: 0.292 sec in AF-C (sports continuous mode)
The D5100's shutter delay is: 0.251 sec in AF-C (sports continuous mode)
(see www.image-resource.com for testing of shutter lag figures)
And this is not even using live view, but the view finder. Add 1.0~1.2sec for using live view in either camera.
If you consider a 90mph fastball travels 13ft in 0.1sec - the same time difference between the D3200 and D5100/D5200, it may make the difference between getting the shot and not. And as the shutter delay exceeds 1sec for live view, you should never use live view for sports and action photography.
Even the D3200's shutter delay is not that great - professional and advanced amateur cameras are in the 0.05 sec range. But the D3200's shutter lag is a whole lot better than the D5100.
If you want sports and action - go with the D3200. If you want video or slower forms of photography such as landscapes or portraiture - then the D5100 would be perhaps better.
Most people do not realize that the "convenience" of that stupid articulated LCD screen carries a heavy penalty in shutter lag. And that penalty is applied even if you are not using Live View.