Home winemakers tend to ferment in glass carboys (big 5-gallon/19-L jars, essentially) because they are usually better-sized and more convenient to a home hobbyist than larger vessels like a 59-gallon (223-L) barrel.
Additionally, carboys are inert, easy to heat or cool (heating pad or cold packs), pretty easy to move around and are especially easy to clean. In fact, they’re clear so you can see if you’ve done a good job. In contrast, a barrel is not easy to clean, is hard to move around and store, is extremely heavy and also is extremely expensive. A good, sound used barrel can cost $200 whereas a brand new French oak barrel will cost $1,000 or more. By comparison, a 5-gallon (19-L) or 6-gallon (23-L) glass carboy will run you around $30 to $50.
Granted, when home winemakers start to make more volume, and especially if they want to emulate styles where oak aging is important, they often do graduate to using barrels. Sometimes you can get 35-gallon (132-L) “half barrels” from barrel suppliers, which will enable the home winemaker to grow a little without committing to the full half-ton purchase of grapes (again, could be another $1,000) that a 59-gallon (223-L) barrel necessitates.
Some home winemakers compromise by fermenting in stainless steel kegs of 5–15 gallons (19–57 L) in volume. Stainless steel can be great, and I’ve often used it, especially for white or pink wines, but since they are opaque it’s sometimes hard to tell visually if you’ve done a good job cleaning and sanitizing. However, homebrewing supply stores do tend to keep a good stock of both kegs and carboys and all the fittings, so you should be able to find a solution that works for you in your home winemaking endeavor.