You need to ask yourself a few questions.
Do you want to design unix systems
Do you want to repair unix systems
Do you want to manage unix systems
Most companies you will do all three, I am seeing however more companies adopting the design, implementation, repair model...
"back in the day" we did cradle to grave system administration build it, maintain it, retire it.... Each aspect requires different skills (with quite a bit of overlap mind you...).
But the most basic trait i can think of is this. When you see a problem and 'think' you know the solution stick with it... in most cases there are about a dozen ways to fix it... if you switch around from solution to solution you could cause yourself more problems. Make lots of notes, you could be working on a problem > 24 hours with a notepad up... you dont have to remember what you tried 22.5 hours ago ;-)