The methods offered in the Pathfinder RPG: Alpha Release on page 12 sidebar Designer Notes: Starting Hit Points are Standard, Double, Racial, Flat, and Constitution. In the past I have ran all of these but the Flat. And I have just play tested Constitution using Pathfinder: Curse of the Crimson Throne – Edge of Anarchy, Part One: Haunted Fortunes.
My fillings on all of methods I have done recently and in the past are as follows:
Standard: We all know that at first level all it takes is a fatal die roll, or even two or three not so fatal die roll, and even the fighter in the party is down or dead. If the person hit is the party healer then the party is in for a bad night and a possible player wipe. Though this method is fine in later levels, for the first five it can be difficult.
Double: A nice and simple method, used to increase starting hit points. Though this does not provide any advantages to play a particular race/class combination. And give high hit die classes too much of an advantage at the lower levels. As the spread leaves a large gap, the party can still encounter problems if the lower hit die classes where targeted.
Racial: Another nice method, this helps give races a more important role in character creation. This is one of my favorite methods. However it seems that Pathfinder is trying to go for the if you choose your classed favored class you will gain more benefits as evidenced in Pathfinder RPG: Alpha Release on page 8 sidebar Favored Class. So this might not be the best method for the rules or feel that Pathfinder is trying to express, as I will mention later.
Flat: A simple and balanced method. I believe that the only way to be fair is to give everyone the same bonus. But again I don't think this is the feel that Pathfinder is trying to express.
Constitution: I found the characters to be mostly over powered. In fact for the adventure I was running I need to up the enemies hit points a bit, I subtracted the Con modifier and add in the Con score to the base hit points of the monsters/NPCs. Using this method at the lower levels gets rid of the sense of survival, as the players know they have enough hit points to take it. So unless your enemies also have the hit points too the possibility of death is greatly removed.
My suggestion, Merge the Double and Racial systems. Here is what I mean.
Half the Racial benefit
Remove the bonus hit point for favored class instead award half the max hit die or 3 (if you go the 3 route this would be also merging in the Flat rate
Here is a link to a level 1 hit point calculator I created in Open Office for all of the above methods so you can see the spread between the many different methods.
If you would like the calculator in a different format let me know and I will publish it as such.