Afternoon :) What a fantastic freebie!
60 litres is actually a really good size for your first tank, not so big that it takes hours to clean and not so small that it's tough to keep the water in good condition.
Yes, it will be too small for goldfish but you could keep a shoal of 6-8 white cloud mountain minnows OR a single male paradise fish depending on your water parameters. You'll need to test the pH to see which fish are suitable. Do you know if your water is soft or hard?
It does take quite a few weeks to prepare it for fish but if you take the time to do it then you can avoid all sorts of problems that are normally associated with new tanks. Have a read of this, it explains the basics.
I would replace the filter media, you just need a couple of normal sponges in there. Don't worry about carbon or zeolite although if your tap water nitrAte is really high then you might need a nitrAte remover.
You'll also need a water test kit. The liquid ones are more accurate and cheaper in the long run than the dipstick kind. You'll need to be able to test for ammonia, nitrIte, nitrAte and pH. One like this will do the job.
Cleaning-wise you are doing the right thing, use really hot water and give it a good clean with a sponge or cloth. Don't use any detergent because it's a bugger to rinse off. Then you're good to go!
HTH, let me know if you need to know anything else.