I'm in a similar situation, having bought the D3200 only at Christmas to make the leap from film cameras.
On the crop-sensor D3200, the Nikon 55-300 is about £300 from most retailers; the 55-200 is about £200, and my deliberation, is the extra 100mm really that worth while?
No simply.
Crop sensors give roughly 50% more reach for a given lens length than on a full-frame or 35mm film camera; and for twenty years, my main 'long' lens on 35mm was a 70-210... and plenty long enough for nie on all I ever did. I had a couple of tele-converters for it, 1.5x and 3x, which bumped it out to a 105-315mm, or a 210-630.... But I rarely 'needed' that sort of reach, and at those kinds of focal lengths, you really have to be on a tripod to avoid camera shake and are restricted to very high shutter speeds, which with tight apartures limited by the adaptor in that lens case, or by the high-ish apartures of suggested kit lenses, means you have to up the ISO a lot, making them a lot less useful than you'd hope.
Meanwhile; the magnification levels make framing very much more critical, and focusing very much more critical, as it will magnify any errors in your shots as well as the subject.
200 on a crop sensor is already the equivilent of a 300 on a full-frame 35mm... so realistically, I have had to think long and hard about whether the extra 100mm is really worth the extra money.... we're talking a lens thats coming close to costing as much as the camera did.....
Being a tightarse.... my bottom line has been to not bother with either.
I was at the town gala yesterday... took some nice pictures of the local air & sea cadets having a cannon race, and I'm sat cropping them all down to get the subjects filling the frame a bit better......
"Oh.... if ONLY I had got that 2 or 300mm lens!" I thought as I tried cropping out a face to find it only 100pixels tall......
Yup.... if only I had that lens, I wouldn't have ANY photo's because we wouldn't have had petrol in the car to GO!
At LEAST I had the Digi-SLR and I dont have to pay for film.... and what I have got, is 6000 x 4000 pixels, not 3000x2000 I would have got from the 'old' digi-compact, or the 1600x1200 I got from the 'old-old' digi-pact' IF I had enough SD card room to shoot at full res on it!
So I have pictures that are big enough I CAN actually crop down and still retain a decent enough IQ, and I have pictures!
On the learning curve? Big leap into SLR photography, and having the ability to use interchangeable lenses, we WANT to have lenses we can interchange.....
BUT... there is a lot more to photography than the hardware; and what you have got in your hand, is already an incredible bit of kit FAR better and far more versatile than a compact camera, and you can do an awful lot with it and still get some brilliant pictures just with what you have.
You don't HAVE to have a longer lens, and having one wont instantly get you better photo's....
And Budget is all.... £200 is a chunk of money.... and for me a fair few days out, where I could be taking photo's..... that's a lot of opportunity to learn to get the best out of what you already have, and a lot of opportunity to get some great photo's.... which spending the money on a lens might curtail..... Of course if the money is there for both? well why not.... but lens likely to give you more to worry about and get to grips with, help you make more bad choices and poor photo's while you learn, and not really be as wonderful as you hope...
Again, back to my days shooting yesterday.... while cropping some snaps, and thinking 'If only'... follow on thought as I came to the next pic in the list.... "Yeah, actually, IF I had another lens, I would have missed this one while swapping lenses!"
NO help what so ever, as to which of the myriad lenses would work on the D3200... needs lens driven focus motor, hence the more expensive ones..... or of the ones out there, which is best..... on which subject, for where you are at, probably irrelevent, they are all more than adequete.... but, more query as to whether its the best investment you might make in your photography, here and now.....
Getting out and using what you got, getting pics, getting experience and learning your camera, is likely to be more beneficial.
Love the camera and the pic quality, by far the best I've ever had ! 
Doing a search on here, this one bellow seems to be a good choice, assuming it would fit my camera. 
