Hi again, TalJechin.
One thing I tell people thinking about experimenting with Linux is that there's no reason
not to try it because experimenting with it is so easy.
Check out
Wubi. It lets you install a partition of Ubuntu under Windows as if it were any other program, and uninstalls like any other program as well. It automatically sets up the boot manager for a dual boot without your having to hassle with partitioning your hard drive, which is easy but potentially confusing for people that just want to try it out.
One great feature is that if your processor is 64-bit but you only have a 32-bit version of Windows, the Ubuntu you install will support 64-bit anyway.
There are a couple of limitations, of course. First, unless they've fixed it recently, you won't be able to set your computer to hibernate. Also, the partition of Ubuntu resides as a very large file in your Windows file system, meaning that Ubuntu will slow down as your Windows file system becomes very fragmented. If you notice any slowdowns, just run the defrag under Windows and you should probably be good to go. Small price to pay for the convenience, however. If you want to completely migrate to Ubuntu, or even a standard dual-boot setup, the transition is easy. Just remember to always back up your files.
As for chess programs, the ones mentioned in this thread are a good start. I haven't tried any of the Chessbase products under Wine, but Scid is excellent in my experience.
Engine matches require a small amount of fiddling. They aren't as push-button as under Fritz. You'll want to look into the recently updated XBoard which may not have made it into the repositories, I haven't checked. It supports many new features for chess engines and matches. If you're really serious, there's another program called Cutechess which you run from the command line. It supports super-fast time controls for engines, such as game in 10 seconds with a 0.1 second increment. These games are useful for chess engine programmers, as they get reliable results of their engine changes very quickly. This may not interest you, of course, but I'll throw it out there.
Installing engines didn't seem any more or less difficult for me than under Windows. The folder hierarchy is easy to understand. For example, you have a /home folder for all of your personal stuff, while all of the system files are elsewhere. Download a file to your desktop, extract it to /home/Chess/Engines, for example, compile it if need be, and then install it under Scid.
Compiling most programs isn't very difficult once you get the hang of it. It's usually just a two or three step process from the command line, ("./configure", "make", "sudo make install", voila). The GNU C compiler, gcc, already comes with every installation. However, if I recall correctly, the C++ compiler called g++ does not come by default. Downloading it from the repository is simple, though. Usually the makefiles supplied with any source code you compile will boil everything down for you to the three commands above. Compiling chess engines is usually just one command, though ("make"). The engine will compile from the source code, and you'll have an executable just sitting there in the folder ready to be installed into Scid. Just be sure to read the "readme" files if there are any special concerns or instructions.
That's all I can think of at the moment, but I hope it was helpful. The Ubuntu community is also wonderfully helpful to newcomers. Usually you can just Google your question and find out that someone has asked it and answered it already.