You can spend as much or as little as you want in your start-up collection for your own private little brewery.  That answer probably isn’t much help to you, though.  The shortest and perhaps the best answer is $200 – $300, and it is likely to include your first batch of beer.  From there on out, each beer will probably cost you between $40 and $50/batch.  After that, I don’t mind saying you can spend as much as you want because you really can, and by then you’ll know enough about what you’re doing to make those choices for yourself.  In the meantime, I’ll tell you exactly what you need to start with.

You can get all of the needed supplies individually, but it will get you off to a good start if you buy a beer kit.  A good beer kit will have supplies in it that you will use for a long time to come.  Avoid the beer kits you’ll find in department and drug stores.  They are targeted toward gift-givers that really don’t know anything about beer and are good for little more than economic stimulation.  Find a brewing or wine-making store; local or otherwise.  They will not only have what you need, but also the expertise to give you some guidance along the way.

Here is what you will need:

Fermentation Vessel.  Your beer kit will come with a food grade plastic bucket with a lid.  For now, your first beers will only be fermenting for a little over a week, so this will work just fine.  For longer brewing beers, meads, and wines, you’ll eventually want to use a glass carboy (giant jug).  When you make this upgrade, this bucket will continue to be very handy for other jobs, such as cleaning and sanitizing.  One day you will find that you cannot have too many carboys.

Fermentation lock.  The fermentation lock, or water lock, holds a small bit of sanitized water (or vodka if you are so inclined) to separate the fermentation vessel’s inside environment from the outside world.  There are countless contaminates that would love to get inside your fermenter.  If you don’t mind sharing that might be okay, but that kind of infection will cause off-flavors and a less than perfect beer.

Bottling Bucket with a spigot, and bottle filler.  Your beer kit will have a second food grade plastic bucket with a predrilled hole in the base for filling bottles.  You will use an inch or two of tubing to connect the bottle filler to the spigot at the base of the bucket.  By inserting the bottle filler into a bottle, pushing the bottle upward onto the trigger will cause your bottle to fill from the bottom up.  This process is used to minimize oxidization of the beer as it is being bottled.

Thermometer.  There will be several moments when you will need to measure the temperature of your concoction.  It wouldn’t hurt to have a couple of these, especially if one of them is glass.  They break easily.

Hydrometer.  This is a fun little measuring device that will give you specific gravity readings of the beer, and help you estimate how much alcohol will result.  You might remember in your high school science class that water has a specific gravity of 1.0.  Anything measuring more than 1.0 will represent fermentable sugars and other flavor contributing solutes.

Racking Cane and tube.  This little siphon will help move your beer from one vessel to another (a process we call racking) while minimizing splashing and excess oxygenation.  Oxygen is good before your yeast is added.  Oxygen is bad after fermentation has started.

Bottle Capper and caps.  With every batch, you’ll need to seal fresh bottle caps onto their temporary homes until some lucky soul feels the need to imbibe your beer.  Each batch of beer, assuming you make about 5 gallons, may yield up to 55 bottles of beer.  Caps usually come by the gross.

Bottles.  As soon as you think you might be interested in making beer, start collecting bottles.  You can buy them for about $13 or $14/case, but most prefer to collect.  It gives you an excuse to try a variety of beers from around the world; if you need an excuse that is.  Keep the brown bottles without the screw-tops.  Most of your best beers will come in these bottles anyway.  Wash them immediately after use so you don’t have dry mold stuck to the bottom of them when you go to use them.

Strainer.  Most brewers like to keep a strainer separate from their kitchens supplies as any oil from last night’s pasta will negatively impact your beer.  You will use this to hold your grain bag while you rinse the goody out and into what will be your beer.  This is not likely to come with your beer kit, but your kitchen strainer might do just fine, especially if it is clean and easy to clean.  Those wire net strainers can really hold some gunk.
2 Gallon Cylindrical Drink Cooler (igloo).  Many first-time instructions suggest you use just any kitchen pot to steep your grains.  For how little it will cost for you to get a small drink cooler, I find it is much easier to hold a constant temperature in a little drink cooler.  Put this little guy on your buying list.

Pots and Spoons.  Set your eyes on a 20 quart stainless steel boiling pot as you’re first main boiling pot. A smaller pot will also be helpful, say about 8-12 quarts.  You’re likely to already have that one in your kitchen.  You’ll need to stir in some ingredients.  A giant stainless steel spoon is preferred by most, but anything you can agitate water with will do just fine.

Sanitizer.  You’ll be using a little bit of sanitizer on every batch of beer you make.  Several varieties are available and each work a little differently.  I have written an entire section on sanitation.  It is just that important.  Actually, if I were to reflect its importance, I would do several sections on sanitation.  In fact, let me take a moment to at least introduce to you how important sanitation is to making good beer.  Sanitize.  Sanitize.  Sanitize.  Also, don’t forget to rid yourself of as many mycobacterial and fungal contaminates as you can.

Grain Bags.  A grain bag is to beer as a tea bag is to tea.  With 1-3 lbs. of grain, it is much easier to fish it out if you can keep most of it inside one of these bags.  You’ll use one of these for each batch of beer you make.

Notebook.  You will want to take notes on everything so you can learn and repeat your successes.  Write down everything.  You’ll find a need to look back on dates, times, ingredients, measurements, and your impressions of the beers you make.  Jot down any peculiarities and occurrences while you were brewing.  It may help you later to understand what happened that contributed to such a great beer.

There you have it.  Add this to your first recipe and prepare to make your first beer.  The more you learn, the more you’ll find a need and a desire for more toys.  Such is the way of any geek I would guess.  I certainly still have some toys on my wish list.