hi and welcome to the forum.
il give you a few pointers as why we use water treatments and why we cycle our tanks before putting fish in there...
basically calcium isnt really a huge factor for fish, not as much as chlorine is. there will be plenty of chlorine in everyones tap water to kill bacteria etc so we dont become ill etc. now chlorine burns the fish's gills and thus makes it harder for them to breath. there are other reasons but this is the main one.
now leaving a tank running for 24hrs wouldn't do a thing, hell leaving it running for 12 months wouldn't do much either. the reason for this is that you need to colonise your filter with friendly bacteria by cycling your tank....there are 2 ways of doing this, fish in cycle and a fishLESS cycle.
now with a fish in cycle you buy some fish that you will expect to die. i mean they may live through it but its doubtful they will live to there maximum age and be 100% healthy and happy. basically what happens here is you buy a tank, set it up, add water and water treatments, heater and filter, gravel / sand and some plants if you like.leave it running for 24hrs JUST to get it to the correct temp etc, then buy some fish suitible for the tank and hope for the best. you will need to do water changes and to help you know when the right time is you buy a water test kit that tests for Ammonia, Nitrates, Nitrites and the ph. each test has a color chart and in a nutshell the darker the color the worse the water conditions are.( depending on kit ) eventually the tank will become cycled. cycled means that there are sufficient bacteria in the filter to cope with the bioload in the tank.
a fishless cycle is almost the same as above apart from there are no fish involved. you buy pure ammonia usually and add it to your tank.you will notice after a while and alot of water tests for ammonia that the ammonia level has dropped from say 5ppm to 4ppm, which means there are bacteria in the filter/s. the cycle continues and you add ammonia until it cycles the set amount of ammonia in 12 hours. when it does its ready for your fish but you cant put loads in the tank in one go, this will cause an ammonia spike and all your hard work was for nothing, it would end up being a fish in cycle which is what we try and avoid.
i havent gone into much detail here but there are threads on the forum about how to cycle your tank.