Level 1
ST 5 PE 5 EN 5 CH 3 IN 9 AG 5 LK 8
Speech, Lockpick, and Repair
Bobblehead (Medicine)
Level 2
Lockpick +6 (37), Speech +1 (28), Repair +1 (40), Explosives +7 (23), Medicine +4 (38)
Intense Training (AG)
Bobblehead (Perception)
Bobblehead (Charisma)
Bobblehead (Intelligence)
Bobblehead (Agility)
Bobblehead (Luck)
Bobblehead (Lockpick)
Bobblehead (Repair)
Bobblehead (Science)
Bobblehead (Small Guns)
Rad Regeneration
Level 3
Speech +1 (32), Repair +2 (60), Explosives +17 (43)
Gun Nut
Ant Sight
Bobblehead (Strength)
Bobblehead (Speech)
Level 4
Lockpick +2 (54), Speech +18 (60)
Educated
Hematophage
Level 5
Lockpick +13 (67), Speech +10 (70)
Gun Nut
Barkskin
Bobblehead (Endurance)
Bobblehead (Big Guns)
Bobblehead (Explosives)
Wired Reflexes
Level 6
Small Guns +5 (46), Lockpick +8 (75), Speech +10 (80)
Toughness
Bobblehead (Barter)
Bobblehead (Melee Weapons)
Bobblehead (Sneak)
Bobblehead (Unarmed)
Level 7
Science +13 (50), Medicine +9 (50), Big Guns +1 (30)
Bloody Mess
Level 8
Sneak +19 (50), Small Guns +4 (50)
Strong Back
Level 9
Energy Weapons +3 (24), Science +10 (60), Medicine +10 (60)
Commando
Level 10
Sneak +4 (54), Small Guns +4 (54), Science +15 (75)
Finesse
Level 11
Sneak +11 (65), Small Guns +11 (65), Energy Weapons +1 (25)
Size Matters
Bobblehead (Energy Weapons)
Level 12
Small Guns +10 (75), Energy Weapons +3 (38), Repair +10 (75)
Silent Running
Level 13
Energy Weapons +22 (60), Melee Weapons +1 (30)
Sniper
Level 14
Sneak +5 (80), Small Guns +5 (80), Energy Weapons +10 (80), Melee Weapons +3 (33)
Cyborg
Level 15
Lockpick +5 (80), Repair +5 (80), Explosives +5 (60), Science +5 (80), Melee Weapons +3 (36)
Lawbringer
Level 16
Unarmed +23 (52)
Better Criticals
Level 17
Energy Weapons +5 (85), Unarmed +18 (70)
Action Boy/Girl
Level 18
Sneak +5 (85), Small Guns +5 (85), Repair +5 (85), Melee Weapons +8 (44)
Paralyzing Palm
Level 19
Sneak +5 (90), Small Guns +5 (90), Energy Weapons +5 (90), Repair +5 (90), Melee Weapons +3 (47)
Life Giver
Level 20
Melee Weapons +23 (70)
Grim Reaper's Sprint
Level 21
Lockpick +5 (85), Science +5 (85), Melee Weapons +10 (80), Medicine +3 (63)
Ninja
Level 22
Barter +1 (26), Medicine +22 (85)
Size Matters
Covert Ops
Power Armor Training
Level 23
Sneak +1 (91), Science +2 (90), Medicine +5 (90), Big Guns +15 (90)
Size Matters
Superior Defender
Ghoul Ecology
Level 24
Sneak +2 (93), Lockpick +2 (90), Repair +6 (96), Barter +1 (27), Science +6 (96), Medicine +6 (96)
Robotics Expert
Level 25
Explosives +23 (83)
Entomologist
Level 26
Unarmed +8 (78), Explosives +7 (90), Melee Weapons +8 (88)
Nerves of Steel
Auto Expert
Booster Shot
Pitt Fighter
Level 27
Unarmed +10 (88), Speech +4 (84), Barter +9 (36)
Warmonger
Level 28
Barter +23 (59)
Pyromaniac
Level 29
Barter +23 (82)
Explorer
Xenotech Expert
Level 30
Sneak +1 (98), Small Guns +1 (98), Energy Weapons +4 (98), Lockpick +3 (97), Unarmed +2 (96), Speech +2 (96), Repair +1 (97), Explosives +2 (96), Barter +4 (96), Science +1 (97), Melee Weapons +2 (96)
Almost Perfect
I don't really focus on gaining exp quickly, that will come later. I let Dogmeat tank for me until I have 2000 caps, then I go get Charon. Usually around level 4 or 5. At 5 I go talk to Abraham Washington and pass his speech challenge so I can get Sydney on my team as well. From then on I don't do her quest, I keep her with me and have a nice little group. You have to baby-sit her a bit but with Dogmeat closing to melee range and Charon and her dishing out the dps from range you can sit back and loot like mad and never take much damage or fire a shot. I watch her constantly and if she is around 50% health I talk to her and give her some stim packs. She gulps them like mad! Where as you can completely head Dogmeat from nearly dead to full health with one, Sydney will take between 4 and 5 at 50% health. I didn't gain a level after 5 until I decided to complete all the side quests. By that time I was sitting on 6k caps and had bought all the useful house items ( workbench, home triage and chem station )
I like to go talk to 3 Dog as on the way you get some power armor that you can repair up ( if you let the tin cans do most of the work, they die readily enough. It's a tough place, the wasteland. I use the armors to repair Charons new duds ). He is now nearly unstoppable in the early game. In fact I have cleared all the subways, discovered and cleared all the buildings, did all the side quests in each area ( Oasis, Greyditch, Moira were priority for the perks ) and all the bobble heads except Energy Weapons by level 10. At 12 I had beat the original games main storyline and had a ridiculous amount of skill points because I had found just over 80 books.
I have confirmed that Sydney stays around when you complete the Washington Monument dish install for 3 Dog. Her and the others will be waiting for you at the base of the monument. I have not confirmed if she stays if you go to rescue dad in the virtual reality machine or any DLC content.