The answers are right. I ride a "Bike Friday" folder, and folders tend to be expensive.
Yes, they are twitchy simply because the lack of rotational stability. But I have gone many miles on my folder. I use mine to throw into a trunk and it works great.
Where I used to live, you needed to put the bike under the seat, which is why I got a folder. But since then, they allocate cars for bike use only, so that point became moot.
I've not ridden one, but I like the look of Strida (belt drive, 1-2 speed) It doesn't fold as small as a Brompton or Bike Friday, but it does fold to the size of a very large umbrella with wheels. It would be a commuter only bike, but it would be cool.
Expect to pay between $500-$1000 US