A lot of people seem to think that using a framework requires you to learn more than if you roll your own. This is only true if you already know how to architecture web applications, in which case you are probably familiar with one or more frameworks anyway.
Learning software architecture is more art than science and all the pattern books in the world will not teach you the things you will learn by working with a good web framework and reading the source.
When I started programming, I wrote all my code myself and in low level languages too. I learned a lot from it, but my programs could have been finished sooner and with better quality if I had used other tools.
When I started writing programs in Rails, I really learned a lot about architecture and programming in general, which I could probably only have learned by reading other people's code. Having to learn how to use the framework correctly forced me to read a lot of code and understanding why it was written that way.
I would recommend that you pick out a good framework and use that (Rails comes to mind). Even if you roll your own, I would recommend that you learn how to use a framework anyway. Inventing things yourself will take much longer than using existing ideas.