Level 1
ST 5 PE 6 EN 5 CH 1 IN 9 AG 7 LK 7
Speech, Sneak, and Small Guns
Bobblehead (Medicine)
Level 2
Lockpick +6 (24), Repair +6 (30), Explosives +7 (25)
Intense Training (LK)
Bobblehead (Intelligence)
Bobblehead (Strength)
Rad Regeneration
Level 3
Lockpick +16 (40), Medicine +4 (40)
Intense Training (AG)
Bobblehead (Lockpick)
Level 4
Sneak +3 (40), Small Guns +3 (40), Lockpick +10 (60), Science +4 (30)
Educated
Bobblehead (Small Guns)
Bobblehead (Luck)
Level 5
Small Guns +9 (60), Lockpick +14 (75)
Comprehension
Bobblehead (Charisma)
Bobblehead (Perception)
Level 6
Sneak +4 (45), Small Guns +10 (70), Science +9 (40)
Toughness
Bobblehead (Science)
Bobblehead (Repair)
Level 7
Sneak +5 (50), Speech +18 (44)
Entomologist
Ant Sight
Level 8
Speech +6 (50), Science +4 (54), Medicine +13 (54)
Strong Back
Bobblehead (Speech)
Bobblehead (Agility)
Level 9
Explosives +11 (41), Science +6 (60), Medicine +6 (60)
Commando
Barkskin
Wired Reflexes
Level 10
Sneak +8 (60), Small Guns +8 (80), Science +7 (67)
Finesse
Hematophage
Level 11
Repair +10 (53), Science +13 (80)
Bloody Mess
Bobblehead (Unarmed)
Bobblehead (Barter)
Level 12
Sneak +10 (80), Small Guns +10 (90), Repair +3 (56)
Silent Running
Bobblehead (Sneak)
Bobblehead (Melee Weapons)
Level 13
Lockpick +1 (80), Unarmed +3 (30), Explosives +19 (60)
Robotics Expert
Level 14
Unarmed +4 (34), Repair +19 (75)
Cyborg
Bobblehead (Energy Weapons)
Bobblehead (Explosives)
Bobblehead (Big Guns)
Level 15
Energy Weapons +7 (50), Unarmed +16 (50)
Sniper
Bobblehead (Endurance)
Level 16
Energy Weapons +10 (60), Unarmed +8 (60), Repair +5 (80)
Better Criticals
Level 17
Energy Weapons +8 (68), Unarmed +10 (70), Repair +5 (85)
Action Boy/Girl
Level 18
Energy Weapons +18 (86), Repair +5 (90)
Intense Training (AG)
Level 19
Energy Weapons +4 (90), Lockpick +14 (94), Big Guns +5 (34)
Life Giver
Level 20
Big Guns +23 (57)
Grim Reaper's Sprint
With the Yew's Charm your speech will be 70 not including books.
With comprehension your prime skills will be 100 ( Small Guns, Sneak, Lock Pick etc. )
I feel this is the best way to get the most skill points in a level 20 build and still have a very strong character.