Instead of changing the rules by giving extra hit points (rather than just HD + Con mod + feats), how about a "hit point pool"? The way it would work would be a number of points that can be applied toward HD rolls.
Let's say the pool has 24 points and you've got three 2nd level characters, a wizard, rogue and barbarian all with Con 10.
At first level, they roll a 2, 6 and 5. The 2 for the wizard is 2 points less than his max of 4 for a d4 roll, so the wizard subtracts 2 points from his pool and effectively gets 4 hit points for his 1st level. The rogue got a 6 out of 6 (d6 hd), so no points are taken out of his pool. The barbarian got a 5 out of 12 (d12 hd), so he takes 7 points out of his pool to get 12 hit points.
The characters now have 4, 6 and 12 hit points at 1st level; with 22, 24 and 17hp left in their hit point pools. For 2nd level, they roll 3, 3, and 10. The wizard takes another 1 point out of his pool to get 8hp at 2nd level, and leaving 21 points in his pool. The rogue takes 3 points out to get 12hp total and have 21 points in his pool. The barbarian takes another 2 points from his pool to get 24hp, and has 15 points remaining in his pool.
Characters get the most hit points for their HD without breaking the rules or even really having to house rule anything like max hp at 1st level or giving a Con score bonus. Depending on how good or bad the HD rolls are, the pool could last for 3-4 levels but will likely be depleted around 6-8th level or so.
Let's say the pool has 24 points and you've got three 2nd level characters, a wizard, rogue and barbarian all with Con 10.
At first level, they roll a 2, 6 and 5. The 2 for the wizard is 2 points less than his max of 4 for a d4 roll, so the wizard subtracts 2 points from his pool and effectively gets 4 hit points for his 1st level. The rogue got a 6 out of 6 (d6 hd), so no points are taken out of his pool. The barbarian got a 5 out of 12 (d12 hd), so he takes 7 points out of his pool to get 12 hit points.
The characters now have 4, 6 and 12 hit points at 1st level; with 22, 24 and 17hp left in their hit point pools. For 2nd level, they roll 3, 3, and 10. The wizard takes another 1 point out of his pool to get 8hp at 2nd level, and leaving 21 points in his pool. The rogue takes 3 points out to get 12hp total and have 21 points in his pool. The barbarian takes another 2 points from his pool to get 24hp, and has 15 points remaining in his pool.
Characters get the most hit points for their HD without breaking the rules or even really having to house rule anything like max hp at 1st level or giving a Con score bonus. Depending on how good or bad the HD rolls are, the pool could last for 3-4 levels but will likely be depleted around 6-8th level or so.