You don't need 2GB VRAM on a lower end or lower-mid-range video card. If the card is relatively weak, more than 1GB is useless 99% of the time and still not required the other 1%.
As for video cards, you get the worst value around $50. As you found out firsthand, you're scraping the bottom of the barrel and won't even get something better than integrated graphics. The price/performance ratio picks up dramatically as you go further over $50, peaking around the $100 price point then leveling off again. Cards that are roughly $100-$150 have the best price/performance ratio. The HD 7770, GTX 750, or the R7 260X, offer the best value right now.
If you have a poor power supply, the GTX 750 is your best option by far.
If you have a nicer power supply, the R7 260X offers the best raw price/performance ratio.
Anything much stronger than those two and you'd start to notice bottleneck issues in certain games on your CPU.