EQUIPMENT
So you want to take up brewing. Congratulations! As a wise man once said, if you give a man a beer, you will quench his thirst for an hour. If you teach a man to brew, you will inspire him to fill his garage and basement with all kinds of brewing equipment.
I will point you to a very concise explanation for brewing your first batch, but before you undertake that, let's review the minimal equipment you will want for a five gallon batch.
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Not absolutely necessary, but very helpful are the following:
3 Piece Airlock - fill with sanitizer or alcohol to allow CO2 to escape the fermentor yet keep bacteria out.
Universal stopper - Fits all three bottles, airlock is inserted in this. Not necessary for bucket with lid, as lid has a hole with a grommet to hold the airlock. You can get sized, solid stoppers; 6.5 gallon glass carboys take a size 6.5, the PET bottles take a size 7