I didn’t read the other posts, so I’m not sure of what advice you’ve been given…
In my opinion, if you want the best PVE build for a solo mage who will occasionally run instances on the trip from 1 – 80 ---- You go Frost.
Arcane really comes into prominence when you get slow. Slow is a deep arcane talent and won’t be accessible for a while. Also, arcane is not very mana efficient. You’ll be drinking a lot of water.
Fire is viable, but unlike frost will not offer you the control and survivability. Fire kills with huge hits. Frost kills with big hits and a lot of control. That might not seem too different, but trust me, it is…
Mobs hit by frost are slowed. You can get in an extra shot as they approach you, you get better CC options… Mobs hit by fire run at you at full speed. Your goal is to kill them before you get hit. This is easier to do with frost.
Frost rotation - Frost Bolt, Frost Bolt, Frost Bolt, Nova, Backup, Frost Bolt – Dead
Fire rotation – Pyro, Fireball, Mob hits you, Fire Blast – Dead.
Just go frost - "In frost we trust"