Because you are looking for story don't focus to much on the system, look at the settings. That is what will make or break your story. If you don't like the setting for say, Vampires: the Masquerade, then you probably don't want to use the system.
On the other hand if you are just looking for a system that lets you modify your characters the way you want them, I would advise trying GURPS. It is one of the better of point buy systems with enough different addons for various types of settings that you will be able to go wild with what type of characters you want.
If you plan for generic fantasy though, use D&D because it is the generic system for it. The best for the story would be 3.5 and using one of the settings. This would be the best known and with a setting already attached you would not need to work at fleshing out the world.
In the end though if you know a system real well use that and don't cheat. The better you know the system the more likely you can get your play to flow which will sound better. If you cheat on things like dice rolls people will know and they will not accept anything else in the story as being a real game which is part of the draw of this type of thing.
If you know a number of systems quite well first know the type of adventure you want and remove any system that does not fit it. Next take the ones that are left and make up your party for them and remove any system that did not let you make the character you wanted. With your party made in a number of systems run a quick fight for each system recording each. Listen to the records for any pauses that go to long or stumbling caused by rules confusion, if you find none you are lying so have a friend who will tell you the truth listen to them and tell you which goes the smoothest. Use that one.