What the role is
A wali's function in the nikah is specific and limited: to protect the interests of the woman under his care and to contract the marriage with her consent. It is not a veto over her life.
Most of what causes friction between a wali and the person in his care is custom rather than obligation. Separating the two early makes everything easier.
Consent is the whole thing
Her consent is a condition of the marriage, not a formality collected afterwards. A previously married woman states it plainly. A virgin's silence has been treated as consent by the scholars, but silence is a poor basis for a marriage and asking her directly is better in every way.
If you find yourself arranging around her rather than with her, stop and correct it. That is the single most common way this goes wrong.
Vetting properly
Ask for references and actually call them. Ask people who have worked with him, not only people related to him.
Ask about income honestly, including debt. This is not rude, it is due diligence, and any serious family expects it.
Ask what he expects of your daughter after the nikah in terms of work, study and where she lives. Get it in writing.
Getting it written down
Anything agreed verbally between two families will be remembered differently within a year. Conditions belong in writing before the contract, and in the contract itself where they are conditions of it.
Where a condition is disputed among the scholars, ask before relying on it rather than after.
General guidance, not a fatwa. Where something is disputed among the scholars we have said so, and you should ask someone you actually learn from rather than relying on a website, including this one.