First level hit points in the rules I wrote are equal to one half the character’s constitution score, rounded up, with the class modifier (+4 for fighters, +2 for clerics, +0 for thieves, -2 for magic-users) added on. So a first level character with a 13 constitution (13/2 = 6.5 or 7) would have 11 hp as a fighter, 9 hp as a cleric, 7 hp as a thief, or 5 hp as a magic-user. And, of course, the minimum hp cannot be less than 1.
When leveling up a d6 is rolled for each class and then the class modifier is added on. Thus a roll of 3 would be 7 more hp for the fighter, 5 for the cleric, 3 for the thief, and 1 for the magic-user. Again, no matter the class modifier or the constitution modifier no one can gain less than 1 hp per level. In addition the ‘minimum 1’ rule is applied after each stage of modification. Thus a magic user with a -2 class mod and a +2 con bonus would apply each in turn: M-U rolls a 2. Class mod drops to 0, but cannot be less that 1 so becomes 1. Con mod increases to 3. Total gain is 3.

For my zero level campaign the rule of character creation is that no dice are rolled. The player picks two abilities that the character is GOOD at, two they are AVERAGE at, and two that they are POOR in. The good abilities count as having a +1 modifier, average have no modifier, and poor have a -1 modifier. Since there are no numeric values, no racial abilities are applied (these show themselves during training to first level is my justification). Each character will also have a choice of background training based on their two good abilities which gives them some basic abilities. In my current playtest I made half a dozen background jobs for each. Each player chooses two jobs from each of their good abilities blindly, then may decide which of the four they want their character to have as their background. Oh, and since I know that the effective scores for each of the good, average, and poor abilities are 13, 10, or 7 I can give them their zero level hit points of 7, 5, or 4 based on their constitution.

There’s more to it, but I’m not going to write a dissertation here. :-p I did a ten part story and rules on my gaming blog that starts here if anyone is interested: http://legendsoflloringhold.blogspot.com/2017/03/starting-at-very-beginning.html?view=sidebar