That there's one of the questions that many of us ask as we progress in the sport, and I do think that it's one important question to get right.
When you've got yourself a nice racket and great sparring partners to train with, the next thing you'll want to do is to get in the flow of the game and not have to worry about the racket strings not performing like you wanted. Think of it like the scope on your sniper rifle - the gun can still kill without it, but get yourself a good one and you're suddenly feeling good about yourself.
So how should one go about choosing the right string for your racket and playing style? Generally, the hard smashers should prefer the higher tension and harder feel (I got this from conversations I've had with the hard smashers). A good tension to try out for hard smashers is 26lbs. If you feel like you can get more out of the strings then increase it by 2lbs at a time till you find yourself struggling to clear to the back court.
That's right, I judge how much tension my arm can handle by how difficult it is to control the full court clears. A nice tension should allow the ease of a full court clear without much work, and yet have the control to place the shuttle neatly to the sidelines as possible.
Once that's settled, the rest of my shots fall into place. If I can control the four corners with ease, that's the tension for me.
For example, I recently acquired a Yonex Voltric 70, which had Yonex BG66 strung at 26lbs. I took it to the court to try out the higher tension (I'm usually on Yonex Nanology 98 @ 24lbs, but we'll leave the different types of string for later on in the conversation), and found that it was really trying to bring the shuttle to the back court.
The games on that day become a tall order for me, having to use more strength to clear and smash, leaving less time for thinking and movement.
Which brings me back to the string tension being all about ease of play. Find a nice string with a nice tension that allows you to place the shuttle to any direction you want, and still achieve a decent amount of power. I'm not a heavy smasher, so I compensated a little with the lower tension.
I guess what I'm trying to say is, whichever makes the games more enjoyable.
As for the types of strings, to me there're only 2 kinds - hard and soft. I'm currently on Yonex Nanology 98 because they feel a little harder than the BG66, and that gives me a little more feel with my lower tension.
How hard or soft you like your string is also a personal preference. All I can say is to give them a try and hope you get to a nice fit before you spend your family fortune on restringing.