Honestly, I wouldn't recommend the Enhanced Edition. You'd be better off getting the regular versions and modding them (if you have the basic savvy needed for that) to high rez. Heck, you could even use a mod that transfers BG1 into BG2's ruleset and essentially merges the two games into one huge game.
But no, EE doesn't contain BG2.
As for a Mage, prepare to suck massive balls for the first 4 levels. It takes until level 5 (which unlocks 3rd level spells) for the Mage to really get going. For level 1, get Sleep. For level 2 get Web. Focus on locking enemies down and showering them with arrows and slingshots. Once you get to level 5 you open up some decent damage spells (hello Fireball!) and your lower level damage spells start to get up there in power. In BG2 is all pays off since Mages are outright broken in that game. The sheer amount of damage and status effects a Mage can pull off is astonishing at higher levels, not to mention that the best way to kill a Mage is to bring your own Mage.
If you're feeling frisky you could try a multiclass of some kind. Cleric/Mage can be fun, what with access to almost all the spells in the game and only a level or two behind the pure classes. Fighter/Mage and Thief/Mage are also solid, with the first offering better health and weapon options, while the other provides extra utility through thief skills (and also more weapon options).
Finally, there's the ultimate Mage cheese build - Make a Human Warrior (yes, you read that right), play him through BG1, import him into BG2, pick the Kensai kit for him (a Warrior variant that gets tons of bonuses to damage and to hit but can't wear armor), then Dual Class him into a Mage. Once your Mage levels catch up, you'll end up with a mid-level Fighter with good damage and you'll eventually catch up to pure Mages in spellcasting.
And then there's the Wild Mage in BG2, which is just ridiculous...