I use the biggest available Big Apples 60x622mm on a bike designed from the ground up to take them, a Kranich from the German firm Utopia-velo. See my bicycle page at
http://coolmainpress.com/BICYCLING.html or download the Kranich section directly at
http://coolmainpress.com/AndreJute'sUtopiaKranich.pdf. The tyres are the absolutely the central design element in that bike, and I arrived at it because I failed to find a trustworthy brazier (only art school welders applied...) for a bike I designed in which the Big Apples would have been absolutely the central design element.
The first thing you need to determine is how wide a Big Apple the fork on your bike will take. Real Balloons <tm> start at 47mm but heavy duty touring Thorns can take bigger. Schwalbe offers include 50mm, 55mm, and I seem to remember a 57mm, and 60mm. All these seemingly small steps add cubic air volume and are most definitely not marginal to your comfort, achieved via the lower pressure you can inflate to with every step in width. There was a German who had the most superb Pedersens constructed for him to sell; he had only one leg and a prosthetic and was acutely sensitive to vibration; he rode in the summer on 60mm Big Apples without mudguards, which wouldn't fit, and in the winter on 50mm with mudguards; he told me it made a very noticeable difference because the volume of air was nearly doubled. Notice the important implication that the wider the tyre, the taller it grows too, and the implications for fitting mudguards.
Ask on the forum here if you don't know how wide your particular fork is.
As for rims, do not for a minute believe ERTRO that balloons work on narrow rims. ERTRO is a trade body, and the manufacturers of rims during the 29er craze couldn't or wouldn't gear up to making wider rims, and bullied their trade body into a lie, that wide rims aren't necessary for balloons. Fitting Big Apples on narrow rims is not only a waste of money but can be dangerous because you have to inflate to a higher pressure; pay attention to what Danneaux has written about rims being split by high inflation.
The minimum width of a rim which will not compromise the promise of the balloon, not only comfort but also high speed security, is 40% of tyre width across the retaining beads (not the outside width of rim). Wider rims in relation to the tyre can allow even lower inflation pressure, which again adds to your comfort and the security.
My 60mm Big Apples ride on 25mm rims specially made for the manufacturer of the bike, which I failed to source when I wanted to build up another wheel. Rigida Big Bulls are a suitable alternative. I inflate once a month to something over two bar, and at the end of the month the pressure can be down to about 1.6 bar; in around 15 years on Big Apples I've had two punctures, one from jumping a curb on a building site, one from riding at 55kph through a large pothole, both of them rider error through an excess of exuberance.
You can find wider rims in the mountain unicycle niche group; Kris Holmes (name given from memory) rims are especially well regarded; a bicycle designer I know weighs 350lbs and he rides Big Apples on these Holmes MUNi rims--and he inflates to around about the same as I do!
Big Apples aren't without a downside. They're heavy and expensive. They lack tread -- they have symbolic tread which doesn't do anything except reassure the traditionalists who haven't yet caught onto the scientific truth that smooth tyres roll further and faster without all that hysteresis of creeping, crawling tread as it deforms and slows you down.
Do not be tempted by the special racing Big Apples which lack the protection layer; they are intended for only one race, presumably if you don't get a puncture before race-end.
One more thing. I don't use the standard Schwalbe Type 19 tubes for balloon tyres, preferring instead the lighter Type 19A Extraleicht. I've never had any indication that they're inferior in service in any way, and they do save some weight; this is a common conclusion for those who try them. But otherwise, the weight of the Big Apples isn't much of an argument against them: they take more energy to get going, sure, but they also keep going without further energy input for a long way because of the barbell effect of their weight at the furthest extent of the spokes. The rollout of Big Apples is absolutely amazing. In any event, if you're a downhill speed freak, the Big Apples' security is more than ample recompense for their weight.
If you're offered a choice, and you can afford it, take the Big Apples with the most expensive belt and compound. They all (except the specialist racer) have the super feature of the special sidewall that was an extra on the early Big Apples. The best compound has an amazing lifespan. At 8500km I noted that my Big Apples were half-worn, despite not being mollycoddled. If you know that previously, excluding only the uncomfortable Marathon Plus, my best mileage on other-brand tyres never reached 2000km per set, you'll understand why I find the longevity of the Big Apples impressive. You can ride the Big Apple's until the colour of the anti-intrusion band can be seen.
The Big Apples are all-round a very special tyre, and a riskless recommendation for almost everyone.