I'm pretty much only a casual viewer as well. I usually tend to watch CSI: LV and CSI:NY episodes if I happen to catch them while zapping through the channels, but I totally hate CSI: Miami: in the beginning it was kind of funny to watch it with my brother only to poke fun at David Caruso/Horatio, but even that got old after a while.
But anyway to actually kind of answer your question: The episodes are pretty standalone so you can really just watch random episodes and don't really have to fear to not getting whats going on. I think there have been some more arc oriented episodes in later seasons, but even those where only a small part of the seasons IIRC.
You might want to check out TrekBBS's sister site Talk CSI
for answers by more dedicated fans.