The current 230Watt power supply will not have enough power or power leads to run an upgraded graphics card so it will be vital to change the power supply, which must be done first.
I don't think it will be necessary to change the current case, it's a fairly standard sized mini tower so it should accept any standard sized power supply and the shorter versions of the GTX960.
Being a small case I'll strongly advise you to look for a fully modular or semi modular power supply of 450 to 500Watts output, more would be pointless. Look for a quality unit from: Antec, Seasonic, Silverstone, FPS (Aurium series), XFX (Pro series), Corsair (but try to avoid the 'CX' and 'VS' series) or Superflower. Do not be tempted into purchasing a cheap 'high output' unit, they're cheap because they're bad.
At least three companies make compact versions of the GTX960; Asus, Gigabyte and EVGA and they look perfect for your system:
http://www.newegg.com/Product/Product.aspx?Item=N82E16814487093
Not too expensive for a modular unit:
http://www.newegg.com/Product/Product.aspx?Item=N82E16817371058