The cost to maintain marine tanks are nearly the same, regardless of size.
For such a small tank you need extra equipment, like a chiller and an auto top off system. Evaporation in that small of a tank over the day will be significant enough to change your salinity enough to kill fish. Larger tanks don't need an top off or generally a chiller, because of the sheer water volume.
In my opinion, if this is your first marine tank, get at least a 30 gallon. If that is out of your budget/patience, don't bother.
For beginners larger tanks are always better, because they are easier to maintain and stability is much better.
If you are, however, SET on a nano tank, I can help you with that.
Lighting-this will effect what you can keep in your tank. Corals need light to live. Standard hoods with compacts will not do the trick. You will want T5HO (high output) lamps. They are the cheapest solution. A good one for a small tank would be the coralife deluxe.
http://www.petmountain.com/product/aqua ... strip.html
You will need marine salt, as well as a hydrometer. A hydrometer measures the amount of salt in the water. You will want to shoot for 1.025. I recommend investing in a refractometer, they are much more accurate than a swinging arm hydrometer.
You will need a heater, a 25w would suffice for a 3g.
You do NOT need a carbon filter for a marine tank. Most of your filtration in such a small tank will be biological. This comes from live rock/live sand. 1 Pound per gallon is the general rule of thumb. You will need flow through the tank though, so you could get something like the koralina nano or another similar powerhead. What I would do is take an aquaclear filter and mod it into a HOB refugium, for the extra water space.
If your shooting to keep fish in the tank, gobys would probably be your only option. Only one, anything more would be too much bioload.
I hope this helped
