I think (or at least hope) that you're misunderstanding the headhunter fees. I'm not aware of any case where a headhunter will charge the candidate a fee, if you run into one who does that's a massive black flag and I'd avoid them like the plague. While their commissions are generally based off of the candidate's starting salary, that's a fee paid by the company to the headhunter, and assuming no one's being shady, it will never come out of the salary itself. The way it's meant to work is that the commission is supposed to act as an incentive for the headhunter to negotiate for a higher starting salary for the candidate, and for the position to be filled faster for the hiring company. Of course, YMMV with how this applies in practice, as it depends on all of the parties involved. The rest of your advice is solid! I just wanted to vouch for headhunters since I've had good experiences.
It's just a bit of nomenclature. I'm differentiating recruiters from headhunters. Recruiters behave the way you describe, getting their commissions from the company. Headhunters charge a percentage of the candidate's salary. Headhunters work at the executive level where jobs are mostly word of mouth. Some candidates are willing to pay them because finding leads can be really difficult at that level. Most people don't have access to a headhunter because they're not at that level, so I probably didn't need to make the distinction. I just wanted to make sure that the OP didn't pay a fee to get a job since the word headhunter was mentioned.I think (or at least hope) that you're misunderstanding the headhunter fees. I'm not aware of any case where a headhunter will charge the candidate a fee, if you run into one who does that's a massive black flag and I'd avoid them like the plague.
I think I should have asked the question of whether or not to get a recruiter instead of a headhunter. I didn't realize that you needed to be at a certain level for a headhunter to be of great help.