Or is faith the means God uses to bestow His grace on the dead sinner, and thus bring him back to life anew -- God's gift of "grace through faith?"
Is faith an act of man or an act of God? Do we "agree to accept" grace or do we "freely receive" grace? Is Grace of man or God?
Yes, smart men/women do believe in Christ for salvation, and you were smart to do so.
The fool has said in his heart there is no God.(Ps.14)
Ofcourse, faith is not a work, so you cannot claim credit for being 'smart' and accepting the free gift (Rom.4:4-5,Lk.17:10)
No more then you can claim credit for obeying God and yielding to Him in your Christian walk (Rom.6:16)
Doing something does not make it a work.