It's only underrated on NS, which doesn't matter because most of the kids shooting Canon here don't even know why they're shooting Canon. Here is where you should go to learn about this camera
http://www.dvxuser.com/V6/forumdisplay.php?143-Nikon-HDSLR
You didn't specify but it looks like you're mainly interested in filming. I wouldn't bother with the 60D for video, but for photos I'd take it over the D5300. The D5300 will give you better image quality, hands down. Better ISO performance, higher resolution, way more dynamic range, more colour depth, the sensor in that thing is the same as the D7100, it's a beast. It also has the larger LCD screen which I'd actually care about for video. The price difference is made up for in that you get a free lens and the ability to borrow another one, and I'm sure you'll be able to find a used one after Christmas now.
Now, if I were you, I would honestly get the Panasonic GH2. You will still be able to use your dad's lenses (although technically you could with the 60D as well), but the GH2 is dirt cheap now which will give you some money to buy more lenses or stabilization. Along with the legendary image quality, I repeat when hacked this thing will blow the Canon or Nikon away, it actually has video features built in to the camera which for me is huge, things like focus peaking, zebras, etc are really nice to have.