Indeed, Salvation is not unconditional or we would be universalists. No where in scripture does it say works save us or add to it.. but you are right, it is not unconditional. It is based on faith through grace .. not works
Eph 2:8 For by grace are ye saved through faith; and that not of yourselves: [it is] the gift of God:
Eph 2:9 Not of works, lest any man should boast.
Jhn 3:14 And as Moses lifted up the serpent in the wilderness, even so must the Son of man be lifted up:
Jhn 3:15 That whosoever believeth in him should not perish, but have eternal life.
Jhn 3:17 For God sent not his Son into the world to condemn the world; but that the world through him might be saved.
Jhn 3:18 He that believeth on him is not condemned: but he that believeth not is condemned already, because he hath not believed in the name of the only begotten Son of God
Jhn 3:36 He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him.
Jhn 5:24 Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life.
Jhn 6:27 Labour not for the meat which perisheth, but for that meat which endureth unto everlasting life, which the Son of man shall give unto you: for him hath God the Father sealed.
Jhn 6:28 Then said they unto him, What shall we do, that we might work the works of God?
Jhn 6:29 Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.