Hi seeto. Capturing does not involve graphics card or display, so no issue.
Editing is usually done using a preview window. faster systems can show a bigger and higher quality preview (also depends on editing program) but slower systems can worst case just show a smaller preview window.
Actually the graphics card and preview part is not the problem for editing HD stuff, it is the processing power needed to convert the highly compressed AVCHD files into RGB frames to display on the monitor. You need a powderful system to get smooth playback of AVCHD footage. For the occasional times I have to edit AVCHD, I would normally convert it to a different codec (called an intermediary codec) that is easier for my system to handle and also does not degrade so much when using effects and filters. Sony Vegas comes with Cineform, Edius comes with Canopus HQ, these are both very good intermediary codecs.
Not sure the best approach for VS11 because I am not familiar with it. I would probably download the free Lagarith lossless codec and try to use that as an intermediary codec. The file size will be pretty huge though, much bigger than AVCHD.
If you haven't chosen a camera yet, I recommend you look at the Canon HV30. It is HDV, therefore tape based, but the quality is superb and HDV files are much easier to edit than AVCHD. Only drawback is that you have to capture the footage in realtime rather than ripping files to hard disk, but if you can live with that it is probably still the best solution available at the moment. Oh and try to get a neutral density filter if you buy an HV30, it really helps when shooting outdoors in bright sunshine. (This applies to nearly all small cams by the way, it's not a point against the HV30).