the video card uses his own ram memory dedicated to the video, this ram is not used by the system pc only for the video card to store whatever information it needs to display images
recent video cards uses DDR5 to get more speed accessing that information, this extremely useful in high resolutions when playing high quality games, also could be helpful when using cad style apps when creating 3d objects or doing some animations, but other than that, it doesn't matter much, you will be able to see dvd movies, flash videos on youtube or just work normally with whatever ram you buy
i still use some old mainboards with pc133 ram shared with a old via video card, it still works well for basic stuff
about pci express 2.0, this is important for you depending what mainboard you have, i had experiences with some video cards not working well with old mainboards, sometimes a bios upgrade was required but in this case i would say that is not a problem
theoretically the video card should be backwards compatible with the previous pci express version and only not gain the extra speed offered by the new pci express standard that your mainboard doesn't have
something you don't mention is if your psu has the enough watts to make the new video card work, sometimes new video cards will use more power and psu will need to deliver more to the video card and if it is a bit limited you can experience stability problems
there is passive cooling and active cooling video cards, with or without a fan, if you don't like noise, i recommend passive cooling video cards, sometimes pasive cooling are cheaper and a bit more weak than the fan cooled version but if you are not going to play heavy games you won't see the difference
about amount of ram, i recommend you to get a video card with 1 gb of ram, you can find video cards with less ram but 1 gb is enough to run most games at 1080p resolutions(this depends on the cpu and system ram too, not only the video card), you could find video cards with more ram but if you are not going to play games at very high resolutions on multiple monitor setups, you won't use it, under normal circumstances you won't use 128 mbs of video ram in your video card so the rest is not used
about amd and nvidia, at the moment, there is more happy nvidia users on linux than amd users but i hear less amd unhappy users on the recent years so it is better for you to get a nvidia than a amd but if you find a good price on a amd card and you want to play on windows with it, amd could be a option
it would be good that if you have a list of possible candidates you let us know and if there is other users here could tell you to get or avoid certain model for a specific reason
