I usually advise getting a quality power supply but I think as long as you stick with low power demanding videocards you should be okay. Look into an RX 460 if you can't find a GTX 750 Ti for less money. If you are going to replace the power supply AND the videocard, do it one component at a time. I'd suggest doing the power supply first. Use your cellphone camera to record the way everything looks and is connected before you disconnect or unplug anything. After switching power supplies, fire up the computer and use it. Game on it, run stress tests. Make sure it's rock solid before you start on the videocard.
edit: to clarify, a 2gb RX 460 which does not require a 6 pin power connector is what you'd want