The only greater expense will be that of buying salt for water changes, which will hardly break the bank on a small tank.
To put it briefly, anyone setting up to run a salt water tank has to be prepared to do lots of research. After all, you are trying to recreate a small piece of the sea in your living room!
Research is good, but for a simple FO none more so than for a FW is necessary, after all, with FW you are trying to recreate a piecde of a lake or river in your house.
I don't want to put you off, because keeping marine tanks is obviously a VERY rewarding hobby, but it is rewarding only if you actually enjoy doing the work and research that goes with it. If your girlfriend (or yourself) is not that interested in how the thing works, but only thinks it would be cute, then I'd take her round the freshwater section of a good aquatics shop and see if anything there takes her fancy.
Why? Because keeping a FW tank is so infinitely simpler than a marine one? Seriously, this is one of my real bug bears. I keep SPS corals in my larger reef and know for a fact I spend much less time on that than I have to on my FW tanks. Compare the work CFC puts into a number of his tanks, or what all the planted people do on their set ups and you will find that FW can be just as demanding as SW.
A FO tank is a piece of cake to setup. the only difference to a FW tank is that you put salt in the water. That is it. Not all tanks are SPS farms remember.
Let's be honest, most marine fish want similar conditions: an SG from 1.018 to 1.026, temp around 24 to 29 degrees C, pH 8.2-8.4. There is far more variety in FW fishes when one considers the soft waters of the Amazon and the hard Great Lakes in Africa.
But note that even a freshwater tank needs a certain amount of research. That's what makes fishkeeping so exciting, trying to understand where the fish you keep came from, what sort of conditions they need.
I would say that both require the same amount of research: the basics of the nitrogen cycle and how to do basic maintenance.