In an ideal world, all bikes would be 1) cheap 2) durable and 3) good to ride. But in the real world you can have only two of those properties. Add factor number 4) folding and you can still pick only two. In other words: cheap folding bikes are both inefficient and shoddy; and whilst you can have a folding or take-apart bike that's great to ride, it'll be more expensive and less durable than an equivalent non-folding bike.
Once you've got over this reality check, and saved up a bit more, you'll find folding or take-apart versions of most sorts of bicycle. The most popular sort however, is the commuter folder, of which it has to be said that a British-made Brompton is the premium example. This sort of bike is designed to fold as quickly and as compactly as possible for rapid access to and from public transport, with no stowage hassles - although some operators will insist that even a Brompton is put in a bag.
With only a few miles to ride at either end of the journey, commuter folders don't have to be particularly efficient or comfortable to still be a whole lot better than walking! Pay enough though, and they can nevertheless be quite good to ride. Some people even tour on Bromptons!
At the other extreme, you have bikes that are designed primarily for performance, that will fold or take apart, but only if they have to. Dismantling may take quite a while and result in a load of bits for which you need a suitcase, but that might not matter when all day or all week is spent riding. Regular steel or Titanium frames built with S&S couplings make the smallest sacrifice to portability.