So, for each 5th level spell slot you give up, you gain an additional +1 to all of your caster levels. Just make sure to level up each of your casting classes for archmage at least once.
It does not say it is the effective caster level with the class you chose to advance. That +1 bonus from Spell Power (take Spell Power at every level for a +5 bonus total) says it is to your effective caster level. However, from the other thread you posted, it looks like you have a ton of casting classes. It is decent for a core campaign, but it sounds like you have access to a lot of additional sources.
I am not a big fan of the archmage class.
