For a kitchen with moisture and your budget, vinyl is honestly your best bet - it's waterproof, way cheaper than the other two, and you can get really convincing wood-look options these days. With $3000-4000, you're looking at luxury vinyl plank (LVP) that feels almost real underfoot and lasts well with kitchen traffic. Laminate looks similar and costs less, but here's the catch: water seeps into the seams and swells the core. It'll fail in a kitchen where you're cooking constantly. Hardwood's beautiful but it's the worst choice for moisture - it warps and cupping happens fast, plus real hardwood in that budget range means lower grades that show damage easily.
The real talk on vinyl: it won't last as long as hardwood (maybe 15-20 years vs 25+ for hardwood), and some people find it feels a bit plasticky. But for a kitchen? You're trading longevity for practicality and budget sense. Installation matters too - vinyl needs a really flat subfloor or every imperfection telegraphs through. Laminate's the same deal. If you go vinyl, budget a bit for professional installation unless your subfloor is already perfect. Hardwood would eat most of your budget on materials alone and then you'd need moisture barriers and constant maintenance in a cooking space.
My honest take: spend the $3000-4000 on quality LVP with good underlayment and save yourself years of worrying about water damage. You'll get something that looks great, performs in a wet environment, and doesn't require the babying that hardwood does.