What are the most common approaches to earn money with a homepage
(i.e. advertising banners,...?

I am thinking about starting an internet business...

And is there a website, list, etc. where you can find business ideas
for a web based business?

You can earn revenue by:

1. Selling advertising banners that appear on your site.  You get
revenue from both the fact the banner appears and from each
"click-through" (when someone clicks on the banner and vists the
advertised site).  You may get additional revenues if the
click-through results in a sale for the advertiser.

2. You can derive revenue from a linking agreement, i.e., you charge
other sites a fee to place a link to their sites on your home page. 
You typcially charge more for a link that appears "above the fold." 
You can also derive revenue by placing links to your homepage on other
sites and then when people click, they are directed to your site where
they must pay money to download content, proceed into the site, etc.

3. You can earn revenue by charging for placement of content on your
site, e.g., charge photographers to place their photos for sale on
your site, charge a commission on sales of products advertised on your
site, engage in consignment sales of goods shown on your homepage.

4. You can sell your own goods and services on your homepage.

5. You can ask for donations or other voluntary contributions to
support the free services your provide on your page.

6. You can sell or lease subdomain space or you can engage in web
hosting.  By the former, assume that you own the domain "hiking.com." 
You could lease someone the right to use the subdomain, e.g.,
shoes.hiking.com or backpacks.hiking.com. (check your agreement with
your registrar/host before you lease out subdomains--the contract may
forbid it).  By the latter, you would lease space on your server to
other sites, either as subdomains or TLD's.

SEX SEX SEX... That is the bottom line ... Proven that the internet
top seller and search terms are regarding sex.
Thanks
Steve