As soon as possible (ideally within the first 30 days if the place you bought it from offers exchanges within that period), make sure your PRS-600 does not suffer from the
dreaded "e-ink fade in sunlight" problem. It doesn't seem to affect every PRS-600, but a number of people have noticed this, including myself. The reader is perfectly usable, even if afflicted. You just need to turn the screen away from the sun each time you turn a page or access a new menu screen. But supposedly, you shouldn't have to put up with this.
Beyond that, I'd recommend a cover, but that's a personal preference. I really like the official Sony cover. It protects the device very nicely and feels good in the hand while reading.
And, if you ever like to read at night, you might consider a bright LED book light. I like the Mighty Bright ones as they seem to have the right color temperature to really bring out the contrast between the text and background on the PRS-600.
I also like using a PSP-style charger. Mine's a "knock-off" made by JSD and seems to work just fine. (Just make sure it's rated to charge a PSP.)
Depending on where your books will be coming from, you may want to learn a few things about different formats and conversion tools. I think Calibre is a "given." It works really well with the PRS-600. Certainly ADE if you're going to be buying books or borrowing them from the library.
Of course you don't have to figure all this stuff out immediately. Take your time and continue asking questions here. There are a lot of helpful, knowledgeable people here!
Enjoy!!