It can be very expensive, depending on what you want to test for. >$1000. If you can, look up news regarding your city water. Most cities test the water carefully, but of course there has been some terrible news about a US town, lately. If you were on a well, it's a whole different story.
Brita filter pitchers don't test for lead. I only found this out after years of using them. The Purel filter on the faucet does, if I spelled that right. They are competing brands. Brita does now make a faucet filter. ( You attach it to the faucet) But, be aware that kids may drink the water in the bathroom, that may not have a filter.
I just lived in a house with a contaminated well, near huge quantities of animal fecal matter.. I was sick, my cats died, but I think that's an unusual story. Groundwater seems to be getting more contaminated.
Find out the reputation of the city water & do some research. Good luck!