I have been playing world of warcraft and the game is choppy when I get into heavily crowded areas I run it on a Compaq Presario AMD Sempron Processor 3100+ 1.81 GHz, 384 RAM with sis 760 video card.

However the minimal requirements for WoW are

Intel Pentium® III 800 MHz or AMD Athlon 800 MHz
512 MB or more of RAM
32 MB 3D graphics card with Hardware Transform and Lighting, such as NVIDIA® GeForce™ 2 class card or above.

I cannot afford to buy both a graphics card and RAM at the same time so I was wondering which one do you think would make the gameplay less choppy. A graphics card or more ram?

The ram and the graphics card are crap as is the CPU (but not much we can do about the CPU)

As its an older pc i doubt youd be able to get a graphics card for it anyways.

Go for the RAM, use something like Crucial Memory (google for it - you tell it your pcs make and model and it tells you what ram will work, you can buy from them too)

sis 760 is not a graphics card, it is integrated graphics and is the reason you only have 384Mb ram available when in fact you will have 512Mb in your system (the difference is utilised by the integrated graphics chip). If you were to buy anything for the system, get a 2nd hand graphics card. This will free up the ram (as well as cpu cycles) and make the game more playable.
Integrated graphics is like air con in a car, it robs power when used and makes things slower.