The LPI exams are more vendor-neutral than most. That being said, I would probably work with both a Red Hat-style distro, such as Fedora or CentOS, and Debian. This will give you a good cross section between the different package styles. The second most important thing that you will need to do is abandon X Windows at some point and learn the command shell and configuring daemons using the vi editor. Yes, there will be X Windows questions on the test, but you will not pass if you are not confortable doing everything from the Bash shell as well. Also do your homework on Regular Expressions.
Also consider a good reference book. I recommend LPIC-1 : Linux Professional Institute Certification Study Guide from Sybex.