[eluser]PhilTem[/eluser]
Even if you used Laravel or CI you would still have to code a load of things by yourself - like the frontend and the backend). Both CI and Laravel are PHP frameworks, i.e. they provide you handy tools so you don't have to write every single line of code necessary like a database class or a PDO.
Therefore I'd say, CI and Laravel are good for your task (even though I don't know what your client's page offers) it will be more important that the code you write will not slow down the page
Deciding between CI and Laravel I cannot help so far because I don't know what your client offers on his/her page. Development may be faster using Laravel since it offers more bundles that you need developed by others. For CI there are a bunch of "bundles" (called sparks) but I personally think, there could be more