Cheryl,
You mentioned an i3 and 4 gigs of ram, I assume its a brand name computer yes? Like Dell or HP, etc etc. If you check your power supply on the inside, or maybe just give the model number of your computer here, we can determine your power supply rating and if its at least 300 to 350watts (more than likely at least 300 for a brand name pc), then you can maybe drop in a more modern video card in there still without any problem. However, if you wanted to get something insane like in the 150 dollar or over range, then yes you'll probably need a new power supply to handle the load.
The next thing is your screen, do you have any idea what your resolution is? maybe just give us the model number of your monitor, and did it come with your computer as a package? like a Dell or HP or Gateway screen. If its 1080p, that'll narrow down what kind of cards you can get, but if its lower than 1080p then there'll be some wiggle room for cheaper video cards since you won't be making the system push such a big image. It also just depends if you want everything running on High or Ultra settings with the particular resolution. Remember, screen size is not the same as resolution, a 20inch monitor can be 720p or even 1080p with certain manufacturers.
Someone mentioned a GT630 above, thats by Nvidia, that would be a good choice over your onboard video from that i3. And GT640 would be even better, but then that will depend on your power supply.