I would not call repenting a "work". Repenting is changing one's mind - realizing that they need Christ and turning to him.
Why would I repent if I had nothing to place my faith in? Why would I repent if I didn't have faith?
The only "work" I have to do, if you want to call it a work is to believe on the only begotten Son.
Then said they unto him, What shall we do, that we might work the works of God? Jesus answered and said unto them, This is the work of God, that ye believe on him whom he hath sent.
To me it's a privilege - not what I would consider "work".
Repentance is a work, it's not just a change in mind but in action.
Acts 26:20 "But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea, and then to the Gentiles, that they should repent and turn to God, and do works meet for repentance."
In Matt 12:41, Jesus was speaking to the Pharisees and said "The men of Nineveh shall rise in judgment with this generation, and shall condemn it: because they repented at the preaching of Jonas; and, behold, a greater than Jonas is here."
If we turn to Jonah 3 where Nineveh repented we find in verse 10 "And God saw their works, that they turned from their evil way; and God repented of the evil, that he had said that he would do unto them; and he did it not."
Repentance is called a work, a work that God saw.
If you put salvation BEFORE the work of repentance, then you are implying the impenitent can be saved in his unrepented/unforgiven sin. Lk 13:3,5 Jsus said repent or perish. The implication is one will perish/not be sved unldess he repents making salvation conditional upon repenting. In Acts 2:38 Peter commanded repentance and the order of the verse has repentance and baptism BEFORE remission of sins(salvation). When they asked Peter what shall we do, Peter did not say "your saved by faith only, now go repent and be baptized".
I agree that belief is a work, Jn 6:27-29. The people aksed Jesus "What shall we do, that we might work the works of God?"
The peole asked what work THEY were to do. Jesus did NOT answer "do no works lest you try to merit your savlation" Instead Jeus gave them the work of belief.
Jsus told them to "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"
Jesus clearly told them to LABOUR - WORK - WORK - WORK for everlasting life which He shall GIVE.
NOtice everlasting life is given, IT'S FREE yet Jesus told them to WORK for it. Obviously the WORK earns NOTHING but is a necessary CONDITION attached to the free gift. Why can't the faith only word nderstand this simple concept?
Lastly, you said "The only "work" I have to do, if you want to call it a work is to believe.."
So belief is a work. Belief saves, Jn 3:16 just as repenting saves, Lk 13:3,5 and confession saved, Mt 10:32,33 and baptism saves, Mk 16:16.
We have:
belief>>>>>>>>>>>>>>saves
repentance>>>>>>>>>>saves
confession>>>>>>>>>>saves
baptism>>>>>>>>>>>>saves
Since there is just ONE way to be saved, no alternatives and the bible does not contradict itself, then the logical implication is that a saving belief INCLUDES the works of repentance, confession and submitting to water baptism.