What's a good small-batch fermentation vessel?

If you are looking for high end, compact fermenter and dispenser at the same time, you might want to look at this one https://www.getvessi.com/

It has built-in temperature control, CO2 pressure controls, a patented sediment removal system, and an integrated tap. It is small in size as well, compact to be used in kitchen and above all, it has an awesome design.

If you want to bottle your beer, you can have an extension for that as well.

I use a 5 Litre PET water bottle which you can get in most supermarkets - I buy mine from an online source (https://www.brewuk.co.uk/5-litre-pet-demi-john.html) but it's the same as water bottles. I put 4 litres in a use a whole packet of dry or wet yeast and always have a blow off. If you don't dry hop and are careful you can get 12 330ml bottles from it. It's not cheap but it's a pretty quick way of making beer.

Most homebrew supply shops sell a two-gallon bucket, which is ideal for one-gallon batches. Midwest Supplies currently includes a drilled lid with grommet for the same price as other HBS charge for just the bucket. But I found that their silk-screened volume markings are sometimes off, so check them yourself.

For anything larger than one-gallon, I use a 4-gallon PET water bottle from Menard's (recycling symbol #1), which runs about $4-6, water included, with a medium, rubber universal carboy stopper. The drawback is that it doesn't fit on standard-height shelves with the airlock.

@baka's advice on 3-gallon Better Bottles is spot on, because the fermenter should fit on shelving units, is a nice form factor, and is the perfect size for either small batches or for splitting a 5-gallon batch.

Go to the grocery store and pick-up a 3 gallon Primo water bottle for about $8. Use the clean-tasting water in your brew, then put your normal carboy topper and airlock on it to ferment. Or you can buy a rubber stopper, drill it, and mod the blue cap that comes on the primo bottle to accept the stopper.

An option I've used for small ferments is Utz pretzel canisters. They're #1 PET plastic, have a wide mouth with a screw top, and are just over 1 gallon. Perfect for test batches. Just drill the lid for an airlock (or use plastic wrap over the mouth) and Bob's your uncle.

I'm currently using a 1 gallon jug (link below), and it's working great. Best of all, it was $5.

http://www.midwestsupplies.com/1-gallon-glass-jug.html

I have one of the Speidel tanks.

http://www.homebrewfinds.com/2011/10/speidel-plastic-fermenters-from-more.html

The 12L Size would be great for small batches.

I've got a 3 gallon better bottle that has worked nicely for a sour beer experiment. I also bought a few 1-gallon glass jugs for a mead experiment. The mead was fermented in a bucket, and then the various fruit and spice additions were added in secondary in the 1-gallon jugs.

I did find with the 3-gallon batch that it takes about as much effort to brew a small batch as a 5-10 gallon batch. It just takes longer to heat/chill the water/wort for the larger batch.

If you want the finished batch size to be 1 gal. you'll need to start with a container larger than that. If that's not much of an issue, you could use a glass gal. jug from wine or apple juice. You can certainly make a 1 gal. batch in a 5 gal. fermenter, too, but due to the headspace you have to be more careful about air getting to it after fermentation is complete.