Have you priced hardwood? I was shocked to discover I could have prefinished oak hardwood, installed, for $6/sqft.

If you're determined to go vinyl or laminate, don't glue. Get a floating click plank.

If you go laminate in kitchen, make sure that it is one that can handle water. I have had regular laminate in the kitchen in the past, and it did not fare well since my husband will spill small amounts of water on the floor and not promptly wipe them up.

No laminate in kitchen! Whew! So that's off the table. That leaves vinyl. The thickest vinyl you can find (more than 6mm should do it) that fits your budget. I'm not sure why you would change out flooring for a small hallway. That sounds counter intuitive. If you work with vinyl, it should handle everything you throw at it...so the change to a new floor in a hallway sounds a little odd.

Vinyl plank 100%

My parents have had Pergo laminate wood floors in their kitchen for over 20 years with no defects. They look practically brand new still. I have LV planks in my beach condo. They don't lock as tight and will show any inperfection there is in your floor. I'd go with laminate over vinyl any day.