I would suggest that you budget $50-$100 per year as a minimum for running your own website. That should cover:
- Domain registration: $10-$20 per year
- Website hosting: $30-$60 per year
- DNS hosting: $0-$10 per year
Since you are spending at $20 to $100 per month for your home internet connection and your computer cost at least several hundred dollars, the costs for running your own website are peanuts in comparison.
Once you get at least 30 pages of quality content posted on your site, sign up for Google AdSense and put ads on your pages. If you keep adding content, you will be able to recoup your costs through ads within a year or two and your website will be self-supporting.
I would suggest that you don't host your website on your home computer. Rather, look for a "shared hosting" plan that costs $3 to $5 per month. 3rd party hosting can be much more reliable and you don't need to rely on dynamic DNS.
If you do host at home, bite the bullet and pay for the dynamic DNS services. DynDns looks like it is $25/year right now. I've used http://zonomi.com/ which is significantly less. Here is a resource that maintains a list of dynamic DNS providers with costs: http://dnslookup.me/dynamic-dns/.