Very small salt water tanks are pretty difficult to maintain. Properly heating/cooling a tank that small is always a challenge -- most heaters aren't adequate enough to maintain a stable temperature in such a small tank, and you might need to wind up investing in a chiller as well. All tanks deal with evaporation, but in a tank that small you have to monitor that daily or the sudden increase in salinity can kill whatever you have in there. As with freshwater aquariums, you have to worry about ammonia and nitrates, and it's very easy to overstock in smaller aquariums. Three gallons is more of a pico tank than a nano, and with picos and nanos there's virtually no room for error.
As far as stocking options go, it really depends on the fish you're aiming to keep. I'm not very well versed in pico tanks, but from what I can tell you're pretty much limited to gobies -- they don't need a lot of space to swim, most of them stay fairly small, they don't have a huge bioload, and they're pretty happy when kept singly. If you're keeping corals you're going to want to make sure you pick a subspecies that's reef safe, though.
If you've never kept saltwater, I'd advise joining a forum specifically for saltwater tanks, looking around for a local fish store that specializes in saltwater fish, and possibly starting a much larger tank until you get the feel for it.