Here, you will find 2 lists: 1) a minimal equipment you will want (and need) for home brewing and 2) some additional equipment. Quick jump:
Minimal Equipment Extra EquipmentMinimal Equipment Needed
What equipment do we need?
The list below is the minimal equipment that you need to brew. You can always add more specialized equipment and make the brewing day easier (see extra equipment section).
Pot
You can use the pot from your kitchen, no need for special one. The usual role you need to follow is at least 10% more than you are planning to brew.
Example: If I plan to brew 10 litters, I will need a minimum 11 litters pot (if the pot will be bigger it is not a problem).
Fermentation bucket (include cap and tap)
This bucket can be plastic (food safe) or steel (stainless, of course) or Glass.
It should allow all the liquid to go in and not too much head space as this head space can contain unwanted organisms that will ruin you beer.
Prep bucket (include tap)
This can be identical to the fermentation bucket (plastic usually) but here we dont need to close it as it is a temporary bucket.
We will use it to move the young beer from the pot and remove as much residue as we can from the boiling pot,
add the corn sugar and use the tap to pure the liquid into the bottles with special equipment (mentioned below)
Plastic faucet
Self explanatory but I must add that it should be cleaned and sterilize after each use.

Breather (Air lock)
Used to allow pressure of CO2 to exit the fermentation bucket and prevent unwanted micro-organism go it the bucket.

Thermometer for liquid use
Another self explanatory item. You will use it a lot.

Hydrometer
We use it to measure the sugars and determent the O.G

Bottle filler stick
Usually plastic that will help us fill the bottle to its right full size. At the bottom of it you have a pressure stopper that you push to the
bottom of the bottle and fill the beer, when you rise it, it will seal the open and prevent from more beer to flow to the bottle.

Sack for malt
When brewing in the BIAB method, we will use it to fill the malt and put in the water, this can be replaced with stainless steel put with holes in it.
We will use it to remove the malt from the liquid and continue to brew.
Disinfectant
There are many types out there and the most important one is that is food safe and friendly. Please, read the label and follow the instruction, no short cuts here!
Syringe
Usually included in the basic kits for home brewing and you will use it to measure liquid like the disinfectant. It will make your life easier in the brew day.
Bottle Caps
Self explanatory item. Usually comes in bags of 100 items per bag.

Bottles
You can buy new bottles or re-use old ones but if you do re-use old ones, make sure to clean them and sterilize them properly.
Beer Bottle Cappers
2 Types of cappers:
Self explanatory item. Usually comes in bags of 100 items per bag.

Self explanatory item. Usually comes in bags of 100 items per bag.

TopHow can I make my brew/bottling day easier?
Some extra equipment to help...
Testing jar
Our worst enemy: contamination. Do not put your hydrometer into the liquid and risk contamination, pue some liquid and test it in the testing jar.

Mixing Paddle
Self explanatory but if you buy one get the stainless steel as the plastic tend to break.

Beer Bottle Racks
Other than convenience, you can do without one. After cleaning/sterilizing the bottles, you put it on to dry. Do not clean/sterilize the bottles too early.

Beer Bottle Washer
It helps cleaning and sterilizing the bottles by 'injecting' water (with sterilizer or not) into the bottle.
