GT 730 is a terrible card. As far as what cards you can use depends more on the power draw of the cards and not the size, since you can either buy a bracket like I linked or rig up something of your own and use a PCIe riser cable to connect it. The best card for your system would probably be a GTX 1050ti, they are low power(some require no PCIe power from the PSU while others require 6pin connectors which are still are below 100 watts and usually only used for additional fans and overclocking). I still think the 1050 low profile is the only card that will physically fit in the case though.
Your system is really not a gaming system, your CPU is an older Intel and if you have an i3 or even an i5 its going to struggle with modern games(i5 wont struggle as much but still no ideal). Another issue is the fact you only have 4GB of RAM, pretty much any modern game will require at least 8GB.