I am using Bootstrap which is using a max-width for it’s largest container of 1200px. However, I have seen other websites appear larger than this, so wondered if this is a good idea to increase this, or is 1200 an ideal width? If I can go bigger, what would be the ideal max-width?
That would depend upon the size of the client screens you expect and the nature of your page design.
A block of text can start to look odd if it is too wide, as it decreases in height. But perhaps you have multiple columns of text, or perhaps it’s a page of tiled images, that may look fine in a wide container. Who knows?
Again, it comes down to content and readability. 1440 could be OK (seems a bit wide to me).
Tell you what. Try this in your css. Change whatever has content blocks in it to something like this which limits your content to a maximum of 65 characters.
div.content { max-width: 65ch; }
Then look at your content at the various widths, and the max text width should be a pretty good indicator of how wide your content should max out at.
Within a Flexbox ‘page’ container I use max-width to force flex items to wrap. Without max-width the flex items could appear on a large monitor as a thin wide row near the top of the browser window.
I also use max-width on the flex items to prevent excessively long lines of text. That is a separate consideration.
In deciding what value to use for the max-width of a ‘page’ container it makes sense to take into account what the content is like and how it would flow on large monitors.
(My default starting point is a max page width of 1500 pixels)