Yes you need a filter, a Fluval 3 one would be good for the time being. You need to read up on the pinned articles in the Beginnger section of the forum, they contain a wealth of very vital info to know on fishkeeping, i particularly advise reading the "Treating and Avoiding New Tank Syndrome" article as it will explain to you how the water quality works in aquariums plus a lot of other stuff like cycling tanks.
A 30litre will surfice for 3 fancy goldfish for the time but they will inevitably outgrow the tank- the average fancy goldfish can easily grow to 6-8inches long, so you should start planning another new tank at some point soon. Ideally, you should have a minimum of 20gals for the first fancy goldfish and 10gallons for every one after that- it may sound a lot right now, but sooner or later your goldfish will start to look very crampt in a 30litre tank. Upgrading to a larger tank in the future will have many bennefets for the fish, from helping reduce stress levels to improving the stability of better water quality and increasing the life expectancy of the fish in the tank
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Filtration is vital for goldfish as they are big waste producers, and the more they poop the more ammonia they produce, which if not dealt with will kill them or make them very sick or generally decrease their life expectancy. An airstone/bubble pump machine is good for increasing the oxygen content in the tank, and can come in very handy during hot weather when the temp of the water in the tank increases and the oxygen content is thus lowered (goldfish are quite demanding fish oxygen-wise), but overal is not as vital as some decent filtration in the tank.
Do you have any dechlorinator/water conditioner?