There are quite a variety of containers that you can use as fermentation vessels. They can be plastic, glass or stainless steel. The purpose of the fermenter is to provide a sealed environment that allows for the escape of carbon dioxide from fermentation, while prohibiting oxygen and airborne contaminents from comming into contact with your wort or must. The stopper and airlock perform this function.
If you are fortunate enough to have a good homebrew/winemaking shop in your area, it should carry the equipment you will need. It should also have a number of options from which to choose.
PLASTIC:
Retail shops generally carry 6-7 gal buckets that are specifically made for fermentation. Some of the newer styles even have volumes printed on the sides. They may even have smaller used pails available that previously held malt extract or honey.
While plastic is your least expensive option, it is less desireable than glass or stainless steel. This is because the plastic is gas permeable, which means that over time oxygen can find its way to your wort/must. The plastic can also retain flavor from previous contents. So far in my experience however, I have not had this problem. Plastic is a good, inexpensive choice, but is best suited for primary fermentation and not long-term storage.
You may be able to find used buckets for free. If decide to look for used plastic containers, make sure they are food grade. If you want to pick up used ones from a restaurant, bakery, etc..., make sure that they don't retain flovor and aroma from the previous contents. For example, it is almost impossible to get the flavor and aroma out of a plastic pail/bucket that held pickles. Another problem with these 'free' buckets is that the sides of the lid has usually been cut to make removal easier for them. Because of this it probably doesn't have an airtight seal anymore. This may be OK for wine during primary fermentation, but I wouldn't recommend it for beer.
If you look around, you may find other sized plastic containers that you can use. I for example have a number of 2 gal bottles that I use for experimental meads. I found them in a surplus catalog. I had been searching for something like this for about two years before finding them. Be vigilant and patient, you may just be rewarded with a great find at a good price.
GLASS:
With glass, you also have many options. Most shops that I have seen carry at least two sizes of carboys (water bottles). Five gallons is the most common, followed by the 6.5-7 gal size. I have six of the 5 gal and one 6.5 gal. plus two 3 gal carboys. Here again you get to use your imagination. Gallon apple juice/cider jugs are great for small experimental wines and meads, beers too although I have yet to make less than 5 gal of beer. I have also found a use for 48 oz juice jars. But, more on that later.
The advantage of glass fermenters is that air (oxygen,bacteria) can't pass through it and won't pick up some flavors like plastic can. The disadvantages of glass is its higher cost and fragility. Plastic is a lot more forgiving when dropped. Glass will not protect its contents from the effects of light, so it is best to store them in a dark place, or cover them with something like a towel.
STAINLESS STEEL:
The most common fermenters made from SS are old soda kegs (3 & 5 gal). Converted beer kegs and bulk food drums are also used by a few with large batches. Custom fermenters can also be fabricated if you have the budget for it.
Stainless can take a lot of abuse, blocks out light, doesn't retain flavors (gaskets will though), and air won't pass through it. If you can afford it, this is the way to go. Just make sure you are dedicated to the hobby before going out and purchasing a lot of expensive dust catchers.
Now that you have an idea of what type of fermenters are available, how do you choose. I guess I have made the assumption that most of you have some access to a homebrew/winemaking shop. If you don't, there are quite a few mail order outfits that would love to send you a catalog. A net search would provide you with a number of online stores. The advantage of being able to go into a store, is that there is someone who can take the time to show you what is available, and make recommendations based on the interests you have.
If you can't do this, or would like to be able to make some considerations before going into a shop, I'll list a number of things for you to think about:
What are you going to make?----Beer generally needs more headspace in a primary fermenter than a wine, mead or cider would. Higher gravity (more fermentable sugar) beers will need more head space in the primary than lower gravity beers will. If you are adding fruit/pulp to the fermenter, you will need to allow for a greater initial volume to get to your final yield.
How much are you going to make?----Most beer and wine kits are designed for 5 gal (20 L) batches. Many mead and fruit wine (country wine) recipes are for 1 gal batches. Don't forget that recipes can be scaled up or down to match your capacity.
How much do you want to spend?----If you are just starting out, it is probably best to go small and basic. This way you can test the waters to see if this hobby is for you, while keeping your costs down. As you gain knowledge, confidence and experience, you will discover where you want to go and how much you want to expand.
How much space do you have?----A few basic components and a couple if 1 gal jugs are fairly easy to stash around the house. Grape presses and three tier brewing systems on the other hand require some space. Sometimes you just don't have room for all of the stuff you would really love to have.
Now that you have had a chance to mull that over, here are some of my thoughts on how you should proceed.
Find people that do what you want to do. If you have a local shop, they would know of any local clubs. Give them a call (check Yellow Pages under homebrew supplies) and go to a meeting. The members should be happy to share their experiences with you, as well as dispensing advice and their own beverages. This may give you additional ideas on where/how to start.
Since we are on the FERMENTER page I would recommend that you start with at least two fermenters. One of them would be a bottling bucket with a spigot at the bottom, this makes bottling much easier. The other could be either glass or plastic, I would recommend glass. The primary fermentation, would be done in the bottling bucket. When fermentation is almost complete (watch the airlock) transfer to the secondary fermenter. I recommend your secondary to be glass, because you can fill it to the base of the neck and eliminate most of the airspace in the fermenter. If you are using a plastic secondary, there would be 1.5 to 2 gal of airspace, which would be less desireable.
What I do, and would recommend to beginners, is to have three fermenters )Iactually have more). I don't use the bottling bucket for fermentation. I do my primary fermentation in plastic, then transfer the near finished ferment to a 5 gal glass carboy. After fermentation is complete, transfer to the bottling bucket (adding priming sugar if applicable) and bottle. As another option, some of my fellow clubmembers carry out primary fermentation in 6.5 gal carboys, and secondary in 5 gal carboys. Its all a matter of preference and price. Stainless Steel should only be considered when you feel that this is a hobby you will stick with.
The preceeding was geared toward 5 gal yields of beer, wine, cider and mead. What are your options if you would prefer to experiment with smaller batches first? Well, as I mentioned earlier, I am also set up to do 1 gal batches also. Getting a 1 gal jug is the easy part, buy some juice and get the jug for 'free'. This is your secondary. The harder part is to find something with a little more volume for the primary fermenter so your final yield will be 1 gal. One option is to split your primary fermentation into two jugs. My preference is to keep it all in one fermenter, so I look for 1.5 to 2 gal containers. The first one I found was a 2 gal "tupperware type' food container. The problem with it, was that the lid did not have an airtight fit. I finally found what I was looking for in a 2 gal bottle through a surplus supplier. Not knowing what it was made of, I ordered two to test. Then I ordered more, not knowing how long they would be available. I use them for meads and fruit wines. This way I can do a lot of experimental batches, while keeping my costs down (verses 5 gal). I make up my initial volume to about 1.5 gal. When fermentation slows down, I rack (transfer) into 1 gal jug, and hopefully also fill up one of my 48 oz jars. The 48 oz jars have several uses for me. The primary use, is for topping up my other fermenters at racking time, to compensate for the sediment that is left behind. I try to rack several of my meads/wines at the same time so I can get the best use from the 48 oz containers. When the work is done, hopefully there is a little left over for me to enjoy. The other use, is to take to a meeting to share with others, my work in progress.
As you can see, there are many options. Starting out you should stick to the basics. Over time you can add to your collection, as I have done, to meet your needs as they develop.
As an additional note, when I mention the use of my 1 gal and 48 oz containers, they are always fitted with a stopper and airlock. Do not recap them with their original cap. This glass is not made to hold contents under pressure, and any additional fermentation with the cap on could cause the jug/jar to explode or break.