You can approach this issue in a number of ways. Most importantly, you need to look at costs. Always remember, you can have something 1) fast, 2) cheap or 3) correctly done, now pick 2.
If you want something fast and cheap, a CMS is great, but it might not be correct for your businesses.
If you want something fast and correctly done, a custom solution might be your answer, but it won't be cheap
If you want something cheap and correctly done, it will take time.
If you have a clear vision of what you want this to do, then I would always suggest a solution that involves customization. A framework is nice, but has it's own set of rules and restrictions, to a point. The most flexible solution is one that is built from the ground up.
IMHO, if I was looking at this solution, I would look at several things:
How much money do I have?
If you don't have much money, a CMS is great. If you're willing and able to do the work yourself, a framework will give you more of a base, but you'll need to spend time/money to get it working.
How soon do I want this to be in operation?
If you want something quickly, CMS will be fastest. Most hosting companies can get one running in a matter of minutes, and you can customise and start going very quickly. A framework (PHP based) will be easier to host that something else (Ruby/Rails, Java/Spring) but will not be nearly as secure or as fast.
What are my top requirements?
Don't use PHP, and keep in mind any pre-built software will have more common vulnerabilities than any custom software. CMS platforms, especially open source, all share vulnerabilities (since the source is published). A framework will have some common vulnerabilities, and the custom built solution will only have the issues you write into it. The nice part is, the more you get away from a set of pre-built published code, the less likely standard issues will be there (as long as you have a reasonable knowledge of what you're doing).
Don't use PHP, it is the slowest language out there right now. Also keep in mind any pre-built software will have to be more flexible and support more use cases, so speed typically will be slower. The more you have that is pre-built and generic (for all consumers of the software) the slower your load times will be. As a side note, do remember that Google does care about load time when considering page rank.
Pre-built is the way to go, the more custom something is, the longer it takes to build.
Pre-built is the cheapest, then frameworks then custom. PHP is the cheapest language (hosting and writing), Java will be most expensive.
Other User/Business requirements
This covers everything from login, to edit, to image management. Basically, what are the business rules you care about most? Does the CMS offer all of the things you need/require? If not, analyse the cost of adding those now, versus the cost of waiting to add them upfront.
Personally, most of my contract work related to development is because a system written in a slow, insecure language (typically PHP) needs to be faster, more flexible and more secure. The problem is, those solutions are more expensive to both build and host. If you can do it yourself, just run some analysis on the business vs the options, or talk to a friend/contractor Business Analyst. The point of the BA job is to understand what you need, and evaluate options for you. Without more information on what you're doing, that's about all I can help with.
Hope this helps, do let me know if this is unclear.