This is kind of a though question since people have different opinions. But in my opinion, on a cropped sensor camera like yours, I would consider a 35mm more of an all-around lens to walk around shooting, while the 50mm more of a portrait lens. They both can serve multiple purposes, but if I had to choose, and portraits was my main concern, the 50mm wins. A must have lens.

Truth be told, those are both on the short side for portraits... Especially the 35mm. When you have a cropped frame (DX) camera, a TRUE 50mm lens has an effective field of view similar to a 75mm lens on a full-frame, or (FX) camera. If your lens is a "DX lens", then it is going to show you a field of view that matches it's focal length. (Example, an 18-55mm DX lens will show you 18-55mm views on your camera. a TRUE (Non DX) "full-frame" lens like the 200mm f/2 Nikon lens will show you an effective 300mm view on your D3200. (200mm lens x 1.5 DX camera crop factor, 200x1.5=300mm effective focal length) Your portrait lenses do flattering things for human faces and perspective around the 85mm & up range. My favorite lenses to do portraits with are: 70-200mm f/2.8 (at the 200mm end), 85mm f/1.4, and my 300mm f/2.8 lenses. (You need lots of room to use the 300mm lens, but they make women's faces look awesome!)

There's a whole bunch of theory behind why, like compression, and perspective manipulations, but I just accept the rule of thumb of 85-300mm are good portrait lengths because of personal trial and error. You can take a nice headshot of someone with a 50mm, no doubt, but I believe that you will be happier with an 85mm f/1.8 or better, an f/1.4 if you can afford it. A GREAT lens is the Nikon 105mm VR MACRO lens. It is a great portrait lens as well as an excellent MACRO/Close-up lens, and you would be hard pressed to find a sharper lens without spending a bit above the $1,000.00 USD range...
My recommendations are: 105mm VR MACRO/MICRO lens. (Does multiple things and is super-sharp!) | 85mm f/1.8 or f/1.4 if your budget allows, but now we're into the thousands of dollars.... | the 70-200mm F/2.8 VRII This is the lens that I use for portraits at events because of the flexibility it offers, and it takes great portraits, almost the equal of the 85mm in my eyes... But again, we're talking almost $2500 for that lens. The 70-300mm VR was a great, relatively inexpensive lens when I had it. It was too slow for me, (I need the speed of f/2.8 for weddings and events in low light when flash is not an option or desired.) but it was a very sharp and nice lens for "general use". Just be sure to use it between 200mm & 300mm for your portraits, and know that you will not have as easy a time separating your subject from the background as you would with the 105mm VR, 70-200mm f.2.8, and definitely not as well as either of the 85mm lenses would.

Best overall purchase go with the 50mm, but if you are on a budget and want to take easy on the pocket then 35mm which is a very good lens for what you want. I hope this helps.

I shoot with a similar Nikon D5200. The 50mm 1.8 was great for both portrait and landscapes on my last vacation. I would however like to purchase the 35mm 1.8 for some wider shots. I did find on my trip that a few times I did need to back up slightly further then I'd like to fit the shot. Overall I am extremely happy with the 50mm I'd just like to add both the 35mm 1.8 as well as the 85mm 1.8 to my equipment.