I would take a look at Knoppix
http://knoppix.org/ as a starting point. CD that will let you play around with linux, without having to install it on your computer. Mandrake
**broken link removed** is a good point to move on next. Graphical installer, automating updates yada yada ...
linuxquestions.org is your friend when it comes to questions about installation or anything else you might be having a hard time with.
No problems on programming pics on Linux. Check out the GNUpic web site
http://www.gnupic.org/ for a comprehensive list of tools :wink: . I am using PiKdev and Hi-Tech PICCLite, parallel port programmer and bootloader. Eagle is also available on Linux
Yes you can write your own programs. The question about what you can not do is tough ... I am not sure about CAD, and PhotoShop type applications (people sometimes have dual boot for that purpose ... personally the Gimp has been sufficient for my 'amateur' requirements).
I would warn you that if you have never experience a *nix environment, it can be a stepp learning curve. But like everything else, once you get there, you would be wandering why you did not do this earlier.
Hope that my 0.02$ has been of use