Were I you, I would start with Django so that I would have an application up and running faster. And then, since Django is open source, start poking around at the internals to see how it works.
I would wait to roll your own web framework until you've had a little more programming time under your belt. Regardless of whether you may be a quick study or not, rolling your own framework is going to have all sorts of strange issues come up, and sometimes it's nice to be able to ask around on a forum, mailing list or IRC for help. Django has one of the largest (if not _the_ largest) Python community; at least as far as currently common frameworks go.
Django is quite nice as a framework as well, it may turn out that it's all you ever need. There are quite a few people out there who use it for every project they work on, with great results.
You shouldn't try to learn a language with an application framework. I also recommend you don't try to learn Python with a web app. The web is a crazy hodge-podge of standards and a web-app is complicated by how many different problem domains it has to contend with. Write some programs to organize your mp3 collection or filter your email or something.
Also, keep in mind that if you haven't done a lot of programming it will take quite a lot of experience before you're writing apps that are maintainable and reliable.
I would wait to roll your own web framework until you've had a little more programming time under your belt. Regardless of whether you may be a quick study or not, rolling your own framework is going to have all sorts of strange issues come up, and sometimes it's nice to be able to ask around on a forum, mailing list or IRC for help. Django has one of the largest (if not _the_ largest) Python community; at least as far as currently common frameworks go.
Django is quite nice as a framework as well, it may turn out that it's all you ever need. There are quite a few people out there who use it for every project they work on, with great results.
[Edit: Changed "webapp" to read "web framework"]