glad you're getting there with the research, but rest assured, you're not the only non-sciency person on here, you'll get it figured out in no time.
in general terms 0.25ppm of ammonia is not fine
this is where it gets a little confusing, just fire away with any questions
As you have 0.25ppm of ammonia and 1ppm of nitrite in your tap water, for now this is the best you can hope for. It’s not brilliant, potentially it could be damaging your fish, but it’s no worse than it would be for a normal fish-in cycle so the tap water does not give me any more cause for concern than the situation you are in anyway. It’s unfortunate; most people in your situation will be able to bring ammonia and nitrite slightly lower than you can, but it’s not the end of the world.
Once your colony of ammonia consuming bacteria starts to grow they will deal with the ammonia produced by the fish, and the ammonia already in the water, likewise for the nitrite consuming bacteria. So once the colonies start to build up the problem will go away by itself, you’ll just have to grow a slightly larger bacteria colony than usual because it has to deal with the fishes waste and the extra 0.25ppm. You don’t need to do anything to do this, the bacteria will grow by themselves, just follow the usual processes for the fish in cycle.
Normally when cycling with fish we say people should try to keep ammonia and nitrite below 0.25ppm, for you this won’t be possible at the moment, so your target is to keep them at 0.25ppm of ammonia and 1ppm of nitrite for the time being. So test your water, if it ever rises up above these levels then do water changes to bring them down, if the levels in the tank are the same as or better than the tap water, then there’s no point changing the water, you won’t achieve anything (although if they stay at this level for some time you’ll want to do a weekly water change as per standard routine maintenance). Once you are nearing the end of your cycle you’ll start to see ammonia and nitrite drop below the level of your tap water, eventually they will get down to 0ppm for both of them. So now you’ll be thinking, well if the water in the tank is 0ppm and the water in the tap is 0.25ppm, why add the tap water cos it’s worse? Well, at this point the filter bacteria will easily be able to cope with the 0.25ppm of ammonia, so when you do a water change you’ll find that if you tested immediately afterwards there would be ammonia present, if you then tested an hour or so later it’d all be gone. So it’s a very short burst of ammonia, but you get all the benefits of regular water changes into the bargain, it’s worth taking the pain of the ammonia for the benefits of the water change. Although as I said before, you may find that a more suitable routine for you is to do 2 smaller water changes each week rather than 1 large one.