First, let's look at your content concerns:
Would GPL require that all the content also be licensed under the GPL?
No, all variations of the GPL has some clause that ensures that any content is excluded from the license. Here is the text used in AGPLv3:
A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an "aggregate" if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation's users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate. (my emphasis)
While the legalize may seem hard to parse, it is just a reminder that copyright law does not regard the content as a derivative work of any program code or markup used to create the layout and functionality for that content. Instead, such a combination is a said to be a mere aggregate and that the copyleft clause of the license does not apply to other parts (i.e. the non-code) of that aggregate.
The cited clause in the AGPL is not really required, as it is just a reminder stating that this separation between content and code is a part of copyright law, but it is helpful to have such a reminder.
It should be noted that such a clause is absent from CC BY-SA. This is because the CC-licenses are created specifically for content. However, you can still refer to copyright law and just state that your content is a mere aggregate and shall not be licensed under any CC-license. However, Creative Commons do not recommend that you use CC-licenses for software, and I agree.
You also want a copyleft license, which means we're left with: GPLv2, GPLv3, and AGPLv3. (CC BY-SA is also copyleft, but it is already deemed unsuitable.)
Since this is for a website, forks may not be distributed, but instead used for alternative web-sites.
As the copyleft clauses in GPLv2 and GPLv3 (and CC BY-SA) only applies in case of re-distribution, they may not be effective making sure a modified website-design being made publicly available. This means that all these licenses are less suitable for a website-design if you care about copyleft.