That's a mini tower. It has the requried x16 PCIe slot, and takes a full size video card, not low profile. Max card length is 7.40 inches, which will be fine for most 1050ti, but rules out the ASUS card at 8.4 inches. I did not check the Gigabyte 1050 ti 4 gb oc length.
Your power supply gives you 240W of 12V, so you have plenty of power for a 1050 ti
Card length and PSI wattage came from
https://www.dell.com/downloads/global/products/optix/en/desktop-optiplex-960-technical-guidebook-en.pdf
Should be as simple as open the case and stick it in, then move your monitor connection from the MB connector to the video card.
UPdate: here is an example of a short 1050 ti that should fit Card Dimensions (L x H)
6.97" x 4.65"...