Hi, in my experience, you don't need a degree to find work as a web designer. I own my own web design/development business and I have never been to University. As a potential employer, I would much rather look at your ability as opposed to any qualification. That said, a qualification can show that you are committed to learning.
Another problem I have with 'web designer' courses is that they are very general (you learn a little about lots of stuff but not enough of each) and by the time you are 'qualified' some of the stuff you have learnt is out of date. The internet is a fast changing environment with new technologies/techniques coming along all the time.
In your position, I would buy a couple of good books.
For starters, I would recommend 'Head First HTML and CSS' by O'Reilly Press, a brilliantly written book that makes learning the basics really easy.
If you want to learn PHP, I would recommend anything by Larry Ullman, again great books.
Subscribe to related magazines (Netmag is very good) and keep up with what's happening with the industry.
As for creating a portfolio, either offer to do a site for a friend in business or just create fictional businesses and create sites for them i.e a dentist's site, a fashion house etc anything that comes to mind. Try and create sites that really show off what you can do.
One final thought, a general knowledge of all related languages/technologies is good, as knowing how the backend of a site is built can help you when designing the front end for example but the best way to get employed by an agency would be to specialise in one particular area. There aren't many people who can claim to be excellent in both design and development, so I wouldn't try, I would choose one area and become excellent in that. This will definitely increase your chances of finding work.
I hope that helps you.
Good luck with whatever you decide to do!