I have zero experience with the NX200 so you're on your own. That said I've never been bothered by write times. Focus times yes, write times no. I believe you will be more limited by the lack of a viewfinder on the NX200 than the write time.
Of the NEX line the 7 is the one to purchase as it has a viewfinder. There are books you can buy on how and why of operation. I bought a NEX and didn't like the processor. It is confused by certain situations but when it nails a scene the NEX is a nice camera.
If you are open to some other cameras, I suggest m4/3. Many of m4/3 cameras are praised for logical operation. You should research them on the m4/3 forum on this site to find out which ones would fit your needs. I like Olympus better than Panasonic. I have a good friend who is just the opposite.
Nikon's V1 might be the perfect camera for you. It is a fast fun to use camera with decent output.
All these recommendations assume you will output to the web, your home printer or computer monitor. All the cameras produce better images than your devices will show.
You can take a card to Best Buy to try out the NEX and V1. I've never seen a Panasonic or Olympus there though.