You should code it however you feel comfortable right now. If you're happy enough coding everything from scratch then do so! If you've never used a PHP (or other language) framework then do you want to spend the time learning the ins and outs of that framework (or in worst case, many frameworks if one doesn't suit you very well) before getting down to work with your applications? Probably not.

Frameworks, by their very nature, speed up development time by providing building blocks. If you have never played with these blocks, don't expect to be building a house (or in this case, a small village!) right away; you'll only end up wondering why your house isn't weatherproof come winter (due to some particular quirk of the framework you choose)!

If you are dead set on using a framework, there are some which are easier to get moving quickly with which you might prefer. Things like CakePHP are targeted towards PHP users of "all levels" (to quote the Cake homepage), for instance. But to be honest, that would be more initial work for you without building anything useful for your applications and, in my view, would skip an essential learning process of doing everything yourself—learning how to keep things separated, to refactor your code out into your own libraries/framework, etc..