So anyway, back to the topic. I think what appeals to me so much about Tales of the Arabian Nights, apart from the great flavor, is that it is an experience game which actually works. Yes, the stories it generates as you have your adventures are usually great fun and the real reward of playing. But you also have to actually play the game. You can't just do stuff because it sounds cool or you want to see what happens; you have to play to your character's strengths, trying to use the skills you've been given or have earned to their best advantage. Courting the Wealthy Princess may sound cool, but if you don't have the Courtly Graces or Seduction skills, it's probably not a percentages play, either from the point of view of winning or generating an interesting story. You have to play to your strengths.
With this in mind, I think a key to enjoying the game is the right attitude. You can't come at it either trying to "generate cool stories" or getting too hung up on winning. I think you have to realize that the game is pretty random, and even if you play the best game possible you may well get hosed. On the other hand, if you don't play to win, you aren't going to generate the most (or even any) interesting stories. So take Knizia's advice to heart, and realize that you do have to play the game to win, but the actual winning itself isn't the important thing.
I'll finish with a couple more concrete tips and observations.
Firstly, on the question of how to choose your victory conditions of story points vs. destiny points: This is a tough call and it's unfortunate that the rules don't give you a little guidance on this, since it's an important decision that you make up-front with little to no information. My sense has been that Story points are a little easier to come by than Destiny, so that argues for favoring Story a little bit. A possibly more important factor, though, is that there is a fairly common status, Scorned, which turns all your Destiny points into Story points. There are also a few other fairly common Statuses that allow you spend Destiny for some effect, and Crippled (which doesn't seem that common) doubles your Story points. On the flip side, Story Point losses, spends, or conversion to Destiny seem very rare (I haven't seen any, but they could be out there). It's still a bit of a shot in the dark, but I think it pays to favor Story points. Scorned seems to come up a lot, and if your objective points are split close to 50/50, it can be a real back-breaker.
Secondly, some folks I've played with have griped a little bit about the early game, a gripe with which I am not unsympathetic. The first phase of the game seems to involve wandering around a bit a trying to make something happen, looking for a break. You're comparatively unskilled at that point, so it doesn't feel like you are able to exert that much control until you've gained some experience. Thematic, but it can make the early game a little unsatisfying. We were pondering minor variants you could use to tweak things a bit, and I think we hit on a good one: just allow the players to pick 4, or even 5 skills at start instead of 3. It seems like it would do no fundamental violence to the game and it would give you a better shot at managing the encounters in the early game, and would let you fit more action in to the same game length. We had a discussion about whether you could get one starting skill at Master level for the cost of two skills, but were undecided. Master level skills are a significant advantage in terms of guiding your destiny, and it seemed like something that should have to be earned. Regardless, personally I don't mind the early game of wandering in the wilderness, but I can see that overall this might improve the game for a lot of folks.
Lastly, keep the player count on this game down. The box advertises up to 6, but that just seems nuts. I'd say you should cap it at 4, and 3 is probably preferable. While you aren't the current player or the reader, Tales of the Arabian Nights is almost pure downtime. There is only so much fun to be had listening to other players' stories. Some, certainly – enough for a 4-player game, I think – but add more players and it gets pretty attenuated.