Stainless pot
$50.00min -- i recommend a 6 gallon. i've done a few brew recipes lately that require what's call a "full boil" where 6 gallons of water are required to boil down to 5.
6.5 gal plastic "Ale" bucket
$10 - $20 -- A good buy for the price to get started. I had one when I began brewing, but replaced it with a 2nd carboy.
Carboy
$30 -- Make sure that it is glass. Also, i've found that when using a carboy, bigger is better. I've got a 5 gallon and a 6 gallon. The larger helps when I dry hop or add other dry ingredients to the final stage of fermentation. The 5 gallon blows off really fast as there is not much space for the CO2 to go.
Air locks & bungs
Less than $5 -- Also pick up about 3' of 3" medical tubing. For the first few days of fermentation, the yeast is VERY active because I start it in a 1 gallon carboy a few days before I brew.
Every time I pitch the yeast, the beer in the carboy (especially when in the 5 gallon) blows out. I've avoided many messes by using a blow off tube with a Home Depot bucket full of sterilized water. After about 5 days, I swap out for an air lock + bung.
Plastic stir spoon
Less than $5 -- When you add the hops, stir the boiling wort very fast. The acidity of the hops causes a reaction with the heat of the malt/grains to create a "whirlpool" effect. This helps oxygenate the wort. However, be careful, as this can cause the wort to boil over and make a huge mess.
Racking tube
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$10 -- Needed for transferring cooled wort (76 degrees is optimal) to carboy.
Just a few more suggestions that I'd recommend:
1. Get a wort chiller. This is a large copper tube in a large spiral used to rapidly cool the wort. Wort that is too hot will kill the yeast. If you've got the coin, get one. It just makes everything easier.
2. Don't use liquid malt extract. This stuff is easy to work with, but it has a very short shelf life. Using bad malt just makes for bad beer. I like using the dry malt extracts. Or, if you want to try, you could do an all-grain method, but that's tough.
3. Keeping everything sterile is priority number 1. Limit any and all chances for bacteria or wild yeasts in the air to get in the beer. I use a mild acid called Star San for all my cleaning and it is sold at All Seasons in Nashville.
4. Keep it simple to start. Maybe even buy a kit to brew your first batch. My most flavorful beers have been recipes, not kits, but the the first few beers I made turned out great and they were kit beers.
I hope this helps.
Happy Brewing!
Sam