Do you feel that WATER baptism has something to do with our salvation? If you say Yes (and I think you will) that would leave a lot of people with no hope. The Bible makes it clear that salvation is all God's doing. I can think of many examples of people in the Bible that were not baptized in WATER and yet they were saved. And would not WATER baptism be a work? And we are not saved by any work, it's all by the grace of God. The Bible talks a lot about baptism, but the baptism that saves is the washing away of our sins and that is something God does. So what do you think?
I have previously answered questions about the necessity of baptism on my web site at two pages, What Does the Bible Say About..Baptism? and What Does the Bible Say About..Baptism and Forgiveness? Some of what I say in answer to your questions repeats or would be amplified by my answers there.
First, you emphasize WATER baptism. In the book of Acts there were only two types of baptism. The baptism of the Holy Spirit, the full coming of the Spirit on a person, only occurred twice, on Pentecost for the apostles (Acts 2) and ten years later on Cornelius and his family (Acts 10). All other instances of baptism were instances of immersion in water. To the average Christian in the first century, baptism would have meant only immersion in water.
Your first question is whether I feel that water baptism has something to do with salvation. Of course, my feelings don't matter; what the Bible says is what matters. But, yes, I believe that water baptism has something to do with salvation, just as I believe that faith and repentance have something to do with salvation. I don't believe that leaves a lot of people with no hope. According to Paul, the only way we would be without hope is if Jesus wasn't crucified and raised again. "If in this life only we have hope in Christ, we are of all men most miserable. But now is Christ risen from the dead." (1 Corinthians 15:19-20) Everyone has hope, if they are willing to obey Christ. If they are not willing to follow him, they have no hope anyway.
In a sense salvation is all God's doing. (I'm not sure the Bible "makes it clear.") In another sense man also has a responsibility in relation to salvation. That is not to say that man can earn salvation by doing things; otherwise "Christ died in vain." (Galatians 2:21) God offers the gift of salvation. But he never promised to save everyone without condition. He says there are those who will be lost. One has to accept his grace, his salvation. Just as a child has to open a birthday present for him to get benefit from it, so we have to "open" God's salvation by meeting the conditions on which he offers it.
You say you can think of many people in the Bible who were saved without baptism. Yes, Jesus told a number of people they were saved. But after the events of Acts 2, after the beginning of the church, you will not find any who were saved without baptism. You may find a few where baptism isn't mentioned, but very few and no indication that they were saved without baptism. Even a Jew could not be saved under the Law of Moses without immersion in water.
Would water baptism be a "work?" That, of course, depends on your definition of "work." If one were to say that God owed them salvation because they had believed, repented, and gotten wet, then they would be wrong. When the Bible (particularly the book of Galatians) talks about "works" it is talking about trusting in complete obedience to a system of law (legalism) to save. But even Paul, when talking about legalistic works says that immersion in water is the same as faith, and is how we "put on Christ." (Galatians 3:26-27) When James says "faith without works is dead," (James 2:17-26) he is using the word in a totally different sense, and is saying that you can not be saved without acting on your faith. James doesn't contradict Paul. Paul says salvation doesn't come through legalism and James says salvation doesn't come through mere acknowledgement that Jesus is the Son of God. Interestingly, most people who object to baptism as a work will admit that one has to have faith before they can be saved. Yet Paul never calls baptism a work, but he does call faith a work (1 Thessalonians 1:3).
Yes! Emphatically Yes! The baptism that saves is the washing away of our sins, and that is something God does. But how does he do it? Paul says in Acts 22:16 that he does it through immersion in water (baptism). Peter says in 1 Peter 3:20-21 that he does it through immersion in water. If I were to give my child a bath and wash away his dirt, I couldn't do it without water. Peter says that baptism is the washing away of sins, and not dirt, but he emphasizes specifically that it is by water.