Haha actually this qns is tied very heavily to your monitor maximum resolution. For eg, if I have a 1080p monitor running in 32-bit colour config, then:
1920x1080=2.07mil pixels
2.07mil pixels x 32 = 66mil bits
66mil bits / 8 = 8.2mil bytes (bit byte con)
8.2mil bytes / 1024 / 1024 = 7.9MB
So theoretically speaking, an 8MB card might be able to display that image. All the extra memory is used to store internal and xformed copies of textures for rendering (like a cache). Hence more memory = your card can hold more high res textures without having to send the same textures over and over again esp in 3d gaming.
But since your use is of not a very intensive nature, 1GB is more enough for non stuttering performance.
Actually for many people, they would not really pay attention to the lots of values listed online as it is too cumbersome to even calculate. However, if you are really interested, I can summarise it here. Memory bandwidth is in fact, the most impt thing here.
Memory bandwidth = Memory Clock (people are most interested in this lol)*Bus Width (only a handful is interested in this)*Ddr Multiplier (no one is interested in this lmao)
Like the popular online analogy, memory clock can be treated like the speed of a car while the bus width can be represented by the no. of lanes on a expressway. The above value is converted from bit to byte by dividing by 8. Theoretically, the higher this number is, the better the card (purely based on figures). However, there is quite a handful of people who purchase cards/monitors and demanded to play aaaaaaaa titles on high freq monitors (above 100hz) at max out settings without really paying attention to monitor resolution and the current hardware limitations. Esp if one is on a certain budget.
*Pardon my constant editing as I am using my phone to access hwz lol.