Quoted

Secondarily, textures are loaded to Video RAM if available in many cases (though not all). If you play at 1680x1050, to reach the "recommended" 128MB the game would need to load about 74MB of textures into Video RAM. Most of the textures will be loaded after Character Select (hence some portion of the loading time) and of course during gameplay when you run into an area that needs other textures, or see other characters with armor that wasnt loaded, etc (hence the lag).
This is exactly what causes lag (low framerates). No question the MORE video ram you have the less you have to go to system ram or hard drive for textures.
Incorrect.

Textures are loaded only into Video and System RAM. They will never be loaded into Virtual Memory, which can be stored on the hard drive in a swap file. The game will never use as much Video RAM as it can. -- it is optimized to only load textures on demand, or it will always load various common textures. There will always be loading times during gameplay, due to this optimization. This is why SSDs make an improvement in texture load times during gameplay. Even if you have a 16GB video card, the game is not going to load all possible textures, by design. If the game did load all textures, your performance when multiboxing would drop simply because the game will be forced to put textures in System RAM when it runs out of Video RAM anyway.

There is no "overkill", get as much on board video ram as you can. BUT ALSO avoid crossfire or sli boards (i.e. boards with 2 gpu in crossfire or sli config). And that gets us right back to the:

Radeon HD 4870 1 GB

http://www.anandtech.com/video/showdoc.aspx?i=3415
There is definitely overkill as far as Video RAM. Just like System RAM, if you never reach 50% in use at any given time, you might as well have 50% less RAM. Therefore, you should determine how much Video RAM you're actually going to use, and if that doesn't reach 1GB in the first place, don't pay a premium just for an extra 1GB on an otherwise identical card.