I've just moved from being a UNIX SA/SE into running a UNIX engineering team for our company. Lots of new hw, and sw wise a mixture of Sol 8/9/10, RHEL, and CentOS.
As for your question of "how you got into it" - I started as a PC/Laser printer engineer, and progressed through different roles - any kind of sw programming and admin was in my own time. I wen to work for Sun as a field engineer in London (hardware), then progressed to be a storage SSE. Moved on to work for various Sun partners doing consultation and installations, then got into a basic sys admin role. Moved to my current employer 2yrs ago as a senior engineer (doing hw and sw, not just sysadmin but applications), then promoted to run the UNIX engineering team 3mnths ago.
Have some interest in hardware as well as software, especially if you want to get into UNIX rather the just Linux, as Solaris/AIX/HP-UX all have tie-ins to hardware. For Linux just learn yourself - spend some time understanding how the os works underneath, and also pickup knowledge on apps (basic stuff like Apache, DNS, networking, LDAP). Being able to demonstrate this kind of stuff will make you attractive to employers. One last thing - learn a couple of decent scripting languages - BASH/KSH shell scripting, and things like Perl, even at a basic level, are really useful.
Good luck