First of all, just a word about cycling. Just running your tank empty with the heater and filter on will not cycle it. You either need to add drops of liquid ammonia or add hardy fish. Or to put it another way, if you have not been adding liquid ammonia, once you start adding fish your tank will still go through the cycle, so you will still need to be careful, adding fish slowly and keeping an eye on the water stats. A liquid test kit is a good investment. And there are good pinned topics on cycling on this forum.
Tiger barbs sound a nice idea. Make sure you keep a good sized school of at least 6-8 to prevent aggression problems as these guys can be a bit nippy. For this reason, they should not be kept with fish with flowing fins (not guppies, bettas etc), nor with timid fish (like some gouramis). As far as I know, tiger barbs are not considered hardy enough to start off a tank- though it's many years since I kept them and I knew little about fishkeeping then.
Hardy fish that are suitable for cycling are danios, as mentioned above, platies and black widow tetras. Danios are spotted or stripy blue and white/golden, black widows are black and white and platies come in all sorts of colours, often with a tendency towards red or orange.
I would follow Anita's recommendations: danios would go well in that tank. Again you need a school of at least 6-8, but that shouldn't be a problem in tank that size. They will appreciate the space you can offer them; because they are so hardy, I think they often get put in tanks far too small for them.
Then you will have a tank with lots of activity at the surface and in the middle. You may want to follow this up with some sort of bottom dweller, something like a bristlenose plec.
I would either do a fishless cycle (as described in pinned topic) or start this tank off with a school of 6-7 danios. Then once the ammonia and nitrites have spiked and gone down again (should take 4-6 weeks), I would add the bristlenose (if you go for that- or something else moderately hardy). Then after a few weeks, if there was no ammonia or nitrite in the tank, I would add the tiger barbs, possibly in two batches.