Here’s an idea – you have your full natural abilities at first level (full point buy), but you haven’t figured out how to best make use of them. Modifiers are “restricted” or “unrestricted” depending on the application. The “restricted” modifiers only apply up to your level. Even with a +4 Str bonus, at first level you only get a +1 to hit and damage. The Int bonus might be unrestricted for skill ranks but restricted for DCs of spells.
Skill checks could be restricted by either your level or your skill ranks (whichever is higher). So the 1st-level Bard with 4 ranks in Diplomacy and an 18 Charisma can add his full +4 Cha bonus as could the 4th-level Fighter with 0 ranks.
This approach constrains the bonuses that make low-level characters so much more powerful than the commoners without saying, “You are average in every way.” It will lead to a rapid scale-up in power from levels 1-4, after which point there will be little if any difference between this system and the rules as written. If you want to stretch it out, say that “restricted” means you can’t apply any bonus more than half your character level.
I’d say you’d be better off not restricting the following: number of skill ranks earned; basic ability checks; checks for skills that are widely known and can be used untrained (Swim, Listen); Con bonus to hit points; carrying capacity; bonus spells known; and Fort saves (given how common disease is, a high-Con level 1 commoner should be visibly more disease-resistant than average).
These could quite reasonably be restricted: most combat modifiers (hit, damage, AC, initiative, grapple/trip/disarm modifiers); spell DCs; checks for more exotic skills (Spellcraft, Disarm Device); Reflex and Will saves; and rage duration.
But keep this in mind: even in OD&D, low-level characters were above the norm. Commoners did not have character classes at all - they were 0-level "Normal Men" and extremely weak (no Con bonus to HP, no feats). Titles like "Veteran" for a 3rd level fighter and "Hero" for 4th suggested that even a low-level PC was still a pretty experienced character compared to the world at large. PCs, NPCs, "commoners," and monsters were all weaker; monsters didn't have ability score bonuses to HP or AC, and only sometimes a bonus to damage. Orcs did d8, I think, and now a CR1 orc can do 1d12+12 per hit, or 3d12+36 on a critical.