You can start brewing at home for as little as hundred dollars if you have a few larger pots already in your kitchen. If you wanted a dedicated 'kit' you're probably looking at somewhere between $150-400 depending on what you want. The cheaper starter kits don't have wort chillers, which I believe are essential to making good homebrew (the faster you can cool down from your boil, the better). If you are handy you can make your own with copper tubing from Home Depot and a couple of clamps for a fraction of the price for a wort chiller. My go-to place for buying beer gear and ingredients is morebeer.com. Great resource, super service, and free shipping on orders over $59.
Be warned that it is can be a very expensive hobby. Once you get rolling there is always a new gizmo out there promising great results (and many of them deliver). I've probably sunk $3k-4k into brewing related equipment over the 18 years I've been brewing, but I have a pretty nice all-grain system now with 10 gallon mash tun, 10 gallon hot liquor tank and sparging setup, 5 fermenters, and a small library of literature on brewing, plus a kegerator that I built.
Wish I had more time to brew, and could drink more of it. I probably end up giving away 75% of what I brew...
You can PM me if you want more specific guidance. I've probably helped about 20 people get into homebrewing over the last 15 years.
Mason