I seem to remember from trips to big aquaria that jellyfish require constantly flowing water in large volumes which is difficult to achieve domestically. I have never heard of keeping jellyfish at home but good luck. I thin you would certainly need a marine setup as Jellyfish are saltwater creatures as opposed to tropical.
Definitely marine. I have a marine aquarium and they are a lot of hard work, not to mention expensive! I have never heard of anyone keeping jellyfish but there's a really good site called reefpark.co.uk with lots of very knowledgeable people you can ask. There are lots of other beautiful creatures you can keep though; I have bright red shrimps and some starfish which never fail to mesmerise my guests!