The first site I worked on was a personal site, a gaming community; which is where I learned the ropes really.
It was back in the 90's, a UBB powered forum (based on Perl, brings back memories).
Doing things like:
1. Creating custom skins taught me about design, html and later css.
2. Installing mods manually and actually paying attention helped me to learn perl, as I started creating my own mods.
3. Then extending to include a front site with news, walkthroughs, guides, game info, galleries and stuff
It actually taught me a lot.
My first real commercial site was a simple brochure style site for an art company. It had a very simple CMS where the studio could add images to the gallery on the front site and edit the text on the front of the site.
At the front is had a homepage with a simple "latest works", an about page, a contact page and a gallery of pictures. You could also request a sale (as they were all original works it was 1 product, 1 possible sale of it); the customer would request the picture and the sale was made offline. It was a local company; a friend knew the owner so it was arranged through that channel; the owner asked my friend if he knew anyone who could do websites, my friend gave him my number and away we went.
I would say something like that is viable as a first project as its quite easy really but has a few simple challenges, like image uploads and loading content dynamically.
Or grabbing something like vbulletin or IPB, setting up a community and modding it, I learned a hell of a lot about how commercial applications work, standards and a heap of other things via that route. Well actually I learned about the W3C at the time from a guy who was helping moderate the forum. He was working for his state government (USA) on their websites and was hot on standards, so was beating me over the head to follow standards and do things properly lol.