To me, it all depends on what you want to brew. If it's a standard lager or ale, I can't understand why anyone would want to homebrew, unless you enjoy the entire process and the satisfaction of doing it yourself. When you figure the initial outlay for equipment, supplies and recipe ingredients, it's not a whole lot cheaper than buying retail. If you love the whole idea of making your own craft beer, or want to make some big not-normally-found style then by all means go for it!
First I would recommend you first get The Complete Joy of Homebrewing and The Homebrewer's Companion by Charlie Papazian. These two are the bibles of homebrewing, especially TCJoH. Read them, learn them, live them- especially the parts about cleaning/sanitizing EVERYTHING, EVERYTIME!
Then find a local homebrew shop or homebrewer's club. They should be a font of information for anyone just starting out (wish I would have gotten involved with a club when I began brewing three years ago).
I've got a homebrew shop about 15 minutes from me and the two owners are young guys who know their stuff, have everything that's needed (or can order it) and will provide all kinds of info regarding brewing. Tell them you're a newbie. If they're worth their salt, they'll bust their butts to make sure you enjoy the process, because that means you're going to be a long-term customer.
Are you planning to bottle or keg? Extract or whole-grain brewing? You have to have the correct equipment ready to go.
Brewing is a process, much like cooking, and you can't really hurry it along. Doing a batch from cleaning equipment, prep, mashing (extracting sugars from grains at medium-high (non boiling) temps), boiling (including hop additions), cooling, agitation, pitching yeast, locking fermenter will take a good chunk of a day (several hours). Then you let it sit a week or two to ferment, depending on the style of brew you make (lagering requires lower temps and longer fermentation, ales are much simpler).
Don't get me wrong, I enjoy brewing. But with so many commercially available craft beers, at halfway decent prices, I can understand why homebrewing has been on a bit of a decline in the past couple years. You should be able to find outstanding beer without having to travel long distances.
Oh, and as for the water, most brewers (home and commercial) use basic tap water. If you have soft or hard water, there are additives available to help alleviate potential problems. If you want to use filtered water, that's fine. But you'll get more off-putting flavors from a lack of sanitation than the H2O.