A search reveals that the term "Half oak barrel" is in common use, but it makes me wonder

what the other half is made of.

Hmm.  Gonna put those barrels on the ground?  Concrete?  A deck?  

Gonna use a drip system?  

I've done most of those.

So here's the scoop.   With a drip system, on a timer, you just need to notice if something has gone wrong.

My Aunt grew Citrus that way for thirty years or so, on a deck, in a barrel on wheels.  Once every decade of so, the barrel became too decrepit, and it needed to be replaced.

I've also raised figs that way.  Barrels over soil.  The fig's roots will grow through the bottom of the barrel.  Eventually, the barrel will rot away.  The fig will be firmly rooted, right where it is.

The Oak Barrels are fairly expensive, and they are mortal.  Nice.  But, perhaps a plastic look-a-like barrel might be better, cheaper, and longer lasting.  I don't know.

Those 55 gallon, black HDPE-PP barrels can be had for approximately 10-15 bucks each, if you buy 10.  They are inobtrusive, and they will outlast Oak barrels by a lot.  Just cut 'em in half, and bore a few holes for drainage.

Someday, you might want to put those trees in the ground.  In the meantime, an occasional shot of Miracle Grow should keep them healthy enough.

A horse trough is also a possibility.  Bigger.  Less portable.  More expensive.  Come in HDPE or PP now.  Do you have a forklift?

Another option is to try columnar apple trees in barrels.  In my experience they do pretty well.  My favorites are North Pole, Scarlet Sentinel, and Golden Sentinel.  These are off patent now, so can be grafted by the hobby grower.  The Urban Apple varieties (Tasty Red and others) might be patented, it's hard to tell, and while they are reportedly quite disease resistant, I don't know yet how they will taste.  I think most nurseries use semidwarfing rootstocks for these but for grafting at home, I would try a more dwarfing type.  North Pole, Scarlet Sentinel and Golden Sentinel are all delicious, as far as I'm concerned.  I used Bud 9 to make some more North Pole and Golden Sentinel.  The North Pole ones are two years old now.  They are still very small, about 18 inches to 3 feet but are sturdy and I think starting to take off and grow.  A more vigorous rootstock might give faster result but overgrow its container sooner.  Bud 9 might be too dwarfing for these, I don't know yet.

Personally I'm trying Bud-9 for a variety of miniature apple trees.  I don't know yet how they will produce, but all of the grafts took and grew well this year.  I would grow them with a post for support and strength, and like John says, not the huge apple varieties.  Again, I would try to use disease resistant varieties to help with success.  PRI type, like Pristine, Wine Crisp, Priscilla, Gold Rush, Crimson Crisp are good for that.  I really love the Pristine apples.  I also have a mid size Wine Crisp tree, very productive and a good tasting apple too.  Liberty is not PRI but is disease resistant, and is supposedly triploid, but mine stayed under 5 feet tall using the M27 root stock, and bore a lot of really good apples for many years.  Liberty is a really good apple.  It's now about 6 or 7 feet feet tall at 20 years old, in the ground.  I think it might be overcoming the dwarfing effect of its rootstock now.   M27 seems usually too dwarfing for my taste which is why I'm trying Bud-9.  I'm also trying Geneva 222 for a couple of trees but don't know yet how it will perform over the long term.