I've finally managed to settle everything down with the Samsung Galaxy S. After I won the item on Ebay for a good price in what was an exercise rather than a serious bid the surprises that followed were anything but expected. First I found that the device is next to useless without an internet connection that allows to link to a (Google) account. So first I tried to connect via Wi-Fi as that appeared as a supported way of accessing the Internet.
I had different experiences with Wi-Fi hardware. First I tried a USB Wi-Fi adapter but that did not support setting it up as an Access Point. Then I bought a wireless router and set that up as an AP. However, it took some time and a whole bunch of different software that did not work, to actually connect the device to the internet. For a while I used FreeProxy for connecting through the PC but most applications ignored the proxy settings, I guess, and simply did not connect to the sites on the Internet.
After suffering through different USB issues, I reinstalled Windows. Removed Windows 7 Ultimane N (wish it burns in Hell) with a regular Ultimate edition and *all* the problems were wiped away. All the devices were recognized correctly, all the software all of a sudden worked miraculously. Fantastic.
Then, after little fiddling around, it turns out that Internet Connection Sharing now worked, as well. So, disabling the proxy and a DHCP server and simply using Windows' ICS made it happen. The phone got an IP address and other settings and all the applications recognized that they now had a working Internet connection.
However, before figuring this out, I was lucky to also find an awesome prepaid plan with CrazyJohn's that I used for testing because it included data. So I used 3G connection for initial account setup and synchronization. Now I ported my number to this plan and am using it regularly. Now I'm getting used to being online almost all the time and having access to emails, maps, books, and other stuff wherever I am.
So, finally it is done. I have 3G network connection on the phone and can also connect through Wi-Fi at home. What a rollercoaster. Only two days ago none of the software worked (including Samsung Kies) so I could neither synchronize my data nor applications and the phone was pretty much a phone and an alarm clock. Now it is slowly becoming my main computing device. With 2x16GB of storage, there is more than enough to have all my important stuff with me at all times.