There's absolutely no OC with that pc. So that's something that can be thrown out as a possible worry.
It's a pre-built. The psu says 300w, but take that with a pinch of salt and count on a more reliable 250w as about as high as you can go total. Figure on @100w for the cpu, @50w for everything else. That'll leave you with roughly 100w maximum allowed gpu size. Smaller being better.
Pretty much a gtx1050ti 4Gb that does not require an additional 6pin power will be your best bet. It's not far behind the 1060 3Gb in performance, but the lack of need of the 6pin power is a serious advantage as it'll run only a max of @75w. Doable.
But that adds a question. If you opt for the 1050ti, that's a final decision. If you opt for something that needs a bigger psu, such as a gtx1060 6Gb and really take advantage of that i7, then you'll have to figure a way to acquire the additional fundage for the new psu.