Personally it took me a month to fully cycle without additional beneficial bacteria from a seeded tank. And while gravel will probably be fine, I've never attempted to grow live plants in anything less than sand.
You need to buy a gravel vacuum for partial water changes, a fresh water master test kit, and Seachem Prime to add to fresh water when you do your water changes. The ammonia found in regular tap water will kill your fish without it. Read up on the nitrogen cycle, and don't listen to the packages/guys at petco when they say to change your filter every week. You'll be getting rid of all the beneficial bacteria that you grew and will keep your tank in a constant cycle. Bad news for your fish, and wallet.
Change the filter media when it is literally falling apart and try to put a bit of the old media in with the new to grow more bacteria. If it's gunky, swish it in old tank water during a water change. Also remoteness carbon in the filter media.
I only use carbon after medicating my tank, as it will eventually leach old toxins into the water if left in too long. Otherwise it's good for a week or so for removing residual meds.
Research your fish, most of all. I run a ten gallon with a single betta and nerite snail, and change the water twice a week. I also have a ton of live plants in there to help maintain water quality as small tanks are easy to crash, and I have had a few disasters when I was starting out.
I'd like to say a single betta, OR a group of 10 neon tetras with a couple of mystery snails, Or a pair of pearl puffers if it's well decorated/planted, OR five or six sparkling gouramis might be a good match.
Again use the time the tank takes to cycle as time to research. You'll save time and heartache for yourself, your kids, and your wallet.