So when creating a responsive design, how big should the maximum width of the container be?
The size of your website should be relative to your content needs and the user's viewport. Sometimes that means limiting the size of website to XX pixels. Sometimes that means a 100% width.
A big issue is line length. Copy lines should be 45-75 characters long, with 66-characters regarded as the ideal. If you cap you lines to that size, yet have a base font-size of 14pt, long blocks of copy are going to fill lost among a lot of negative space. To counter this you can increase your font-size to 18 or 21pt. Yet even there though you can't go too much larger because your vertical height will start to be too large. Which means users will have to scroll more.
Just remember that if you're making your website 100%, you need to scale things accordingly - not just the grid. Making your website's layout responsive is important, but that's just a facet of RWD. Making your content scale accordingly is more important.
A web page ideal width is the relative size 100 percent. It would make a great opportunity for you and your design team to work on mobile friendly or responsive design. It a tough approach since you have to address screen that are extremely wide, but implemented correct it is your best option.
In detail you can add left and right padding, add another column when viewport expands, or whatever your design team finds pleasing. The same idea works when the viewport gets smaller; move a column, decrease padding…