Many folks use their tap water and in fish only tanks, it is probably fine-this is usually to avoid the cost of purchasing water, an Ro unit, and the waste water from that if you have to pay for your water fromthe city.
The biggest problem is that you have no control over the condition/contaminates that may exist in the water that could build up in your tank. There could be phosphates or Nitrates already in your tap water, not to mention metals.
But, in prior years, I always used tap water, just aerated it for a minimum of 24 hours and made sure the temp and SG were the same as the existing water in the tank.
YOu will probably have algae-both red and green, but even using RO water, you will most likely go through a browndiatom stage-its normal, dont panic-and will pass.
It takes many many water changes to dilute the intitial tank fill as you are only replacing a small part of the water, which mixes with the existing water.
My suggestion is that if money is an issue-as it often is-Use your tap water, premix and aerate your salt mix as well as using a dechlorinater with a detoxifier in it for any metals.
Your local fish store may test for phospgates and copper etc. in your tap water, but will probably charge you as the test solutions are expensive.
Do you have your own test kits for the cycling? You will need AMmo, Nitrate and Nitrite at least and it wouldnt hurt to have a phophate test kit as well.