If random hit points must be kept (and I'd honestly like to see hit points die in favor of a toughness save or something, then go ala Iron Heroes, but rephrase it. Call the +1d4 "bonus hit points". That makes it seem like an extra that you don't need, but a little something more. Then even rolling a 1 seems decent and not "crippling".
Barbarians get 8 hit points per level, plus 1d4 bonus hit points.
Fighters get 6 hit points per level, plus 1d4 bonus hit points.
Clerics get 4 hit points per level, plus 1d4 bonus hit points.
Wizards get 2 hit points per level, plus 1d4 bonus hit points.
To be honest, I can't fathom how you'd need random hit points to distinguish between two characters in 3.Xe or later. Back in the day when that and ability scores were all there was between Bob's fighting-man and Jim's fighting-man? Sure. But now when Bob's fighter can be specialized in spring-attacking and crowd control with his spear while Jim's fighter is a heavier sword-and-board tank... I don't think that random hit points are really needed anymore.