Something about ammonia and its toxicity.
0.25ppm ammonia is basically 0. Depending on your test 0ppm ammonia might look the same as slight ammonia test. Try testing some bottled water that you know is 0ppm and compare it with your tap water and tank water.
If your tap water is testing positive for ammonia, its probably treated with chloramine rather than chlorine. Chloramine breaks down to chlorine and ammonia once it leaves the tap. In a cycled tank the ammonia will be removed very quickly. The chlorine will be neutralised by your water conditioner. As autumnsky has suggested, using prime as your water conditioner will also detoxify ammonia while your cycle processes it out.
The ammonia you are reading in your test isnt as toxic as you might have been led to believe. Free ammonia is very toxic in even very small amounts. But, your test isnt for free ammonia, it detects total ammonia nitrogen (TAN) which is free ammonia + ammonium. The proportion of free ammonia to ammonium is determined by the waters pH and temperature. The higher the are, the higher the free ammonia is and lower ammonium. At typical aquarium temperatures you need a very high pH before the low levels of TAN you are seeing becomes toxic to fish. Table attached showing TAN toxicity at the level you are seeing. Green is safe, yellow start to take action, red is immediate action needed.
As i have said previously, you want to be trying to keep ammonia + nitrite combined at around 0.5ppm. A little ammonia from your tap might complicate things, but if you change water at the slightest hint of ammonia you will never have enough in there to cycle the tank and will forever be doing daily water changes. Cycling the tank will take weeks at best.
Link to post explaining ammonia toxicity in more detail if you are interested.
https://www.aquariumadvice.com/forums/f12/your-guide-to-ammonia-toxicity-159994.html
Many people have tap water treated with chloramine rather than chlorine and manage to keep fish just fine. As with anyone else, its important to manage ammonia through getting your tank cycled.