Personally I would advise doing illusion, divination or abjuration school for the utility and better class features. Ive never been a fan of the fact that all of the bladesingers features are tied to the songrage, even barbarians get other stuff. This also opens up your options for races, my reccomendation is halfling. a classic rogue race for good reason, both lightfoot and stout are excellent for different reasons.
One level in fighter for shields and the duelling style will make up for that 2 ac during song and not have a time limit. The fighter shield thing is optional and basicalli requires warcaster so it isnt a cheap option.
Other great races include gnomes and vhuman, for your feat grab one of the half feats that gives int or dex, that way you have a +2/+1 and half a feat.