Agreed, make sure the buckets are made from food grade plastic. Commercial grade usually isn't good enough for home brewing (holds bacteria more easily, can leach compounds depending on the plastic, etc.).
Any restaurant should be able to hook you up with 5-10 gallon food grade buckets. Fast food restaurants toss them out all the time. My DW owns a dairy queen, and I have quite a few 10 gallon food grade buckets that used to hold frozen strawberry topping. Bakeries also go through a lot of food grade buckets, too. Talk to the owners/managers and ask them to save you a few buckets and give you a call to pick them up.
The hydrometer is a required item IMHO, it's the only way to tell when your beer is done fermenting and how much alcohol is in it.
Other items I use a lot:
A meat thermometer: In the boil, it reads the temperature constantly. Mine has a handy clip that can clip to the side of my brew pot.
A LCD thermometer: one of those plastic strip thermometers for aquariums. Stick it on the outside of your primary fermentation bucket so you can monitor the beer's temperature while it ferments.
A mesh strainer: A large one that will rest on top of the fermenter buckets. This is for removing hops and other adjuncts from the wort, and it helps aerate the wort as it's being poured into the bucket.
That's about it. Other items are optional.
One item I couldn't brew without in my area is a drop freezer. I live in Florida, and it gets incredibly hot here all year around. Without my drop freezer (and temperature controller), I couldn't keep the beer cold enough to ferment the beer without off flavors developing. Now, I brew the wort, pitch the yeast, and set the fermentation bucket right into the freezer and set the temperature right where I want it (usually right at the low end of that particular yeast's temperature range).