My experience with the Coopers kits are that they produce a beer that is too low in alcohol.. i.e. real session beers. They were ok.. but, once you get a few under your belt, you might want to check out what an IPA, for instance, should be for an ABV range and ramp up the kit with either a little LME or DME. That said, if you like kits for getting your feet wet, I've found Brewers Best to be pretty darn good. Northern Brewer, Midwest and Austin all produce good kits. My all time favorite extract kits come from MoreBeer in CA. I think they've done their research on them.. not to say the others haven't. They have inexpensive and more expensive kits based on ingredients.. pull the trigger on what floats your boat

One thing about their kits is that they are FRESH.. Haven't been sitting around a long time. Time has an effect on extract and hops. Same with yeast.
Regarding using tap water. Might be ok.. depending the makeup of your water. If you use tap water, you'll want to either boil it ahead of time or use a Camden tablet to remove chlorine or chloramines, depending on what your city uses You'll gain more experience with this part of brewing.. for some (me included) it's really a learning process.. but I'm an old fart and am a visual learner.. don't do book learning very well.
Some of my first beers used RO water.. left a bit to be desired. Then I went with 1/2 tap and 1/2 tap water.. that was much better. I going to try a few batches using spring water. We have a spring about 30 miles away that supplies spring water to a major spring water distributer.. just uphill from where they get it. I've only brewed with it once.. at a National Brew Day and my group's extract beer was the favorite of all the beers.. both all grain and extract... that may say something.. Purchasing water can be expensive. One place I can get this spring water is at the Dollar Store.. $1/g.. Possibly using a mix of spring water and dechlorinated tap water will be good for your process. Fortunately, you are brewing extract right now so you don't have to worry about chemistry.
Sometimes, even with extract brewing, adding a tsp of gypsum helps beers like IPA and APA's.. different for malty beers tho.
Keep at it.. you'll make beer.. and each batch will be better.