which cards are you specifically looking at (i.e., Diamond ATI 6450 1 GB, HIS 6450 2 GB, Zotac GT610 1GB)? maybe that'll help you narrow the choices down rather than just picking OEM designs (i.e., ATI 6450, ATI 5450, Nvidia GT610). most cards nowadays come with 1 GB and up. so I wouldn't get less than 1 GB.
it depends on how much you want to save and how long you plan to keep the card. if you're the type to rarely upgrade your hardware, you want as new as possible, especially with regards to graphics technology since graphics technology evolves so quickly. each generation, both ATI and Nvidia keep upgrading their video decoding engine in order to fix bugs and inefficiencies that were unforseen in the previous gen. in an old system, what you're focusing on is the ability to play back videos smoothly and to have a smooth computing experience. You're not so focused on performance metrics such as how many texels/second or how many pixel pipelines the cards has or whatever.
So even though an older gen card might play games better than the low-end newer-generation card, the newer generation card will have the updated video decoding engines as well as the updated DirectX instructions that come with Windows 8. And these are what you look for in terms of an old system which is focused on videos and general user interface smoothness.
Also, it highly depends on what you use this system for. Because all the cards in the low-end market are fairly equal with just some minor differences, (which may be important depending on what your needs are). The key is getting a current-generation or next-generation model. Especially because you want a card that will continue to get new drivers. As a card gets older and older, it eventually gets lumped into the legacy cards category and will receive no further updates.