Core set Arena rocks!
I wouldnt buy anything else for starters.
If you and your kids get into the game and if you start playing vs others you might want to buy some more MW stuff.
The only thing i would advice against is Spell Tome I and II - nothing new and i think your better of buyung an extra core set (as you already did)
Theres a lot of expansions - all of them good - main reason to buy them are to try new mages, new creatures, new cards and tactics. No need at all in your current situation.
Academy is a much shorter game without any movement. Very different from Arena.
Main difference is from 1 and 2 edition is some of the cards got an errata.
Battle Fury (only Melee bonuses on first attack)
Hand of Bim-Shalla (only 1 in play for each player at a time)
Tempel of Light (you have to pay mana for extra dice)
There should be errata cards and info around here.
Box is smaller and the Arena playing map is foldable - which makes transportation easier, but are not as good as the old ones. (zone borders hard to tell apart/sliding the cards becomes harder)
You could try out the playing mats - they are amazing