Flooring removal and replacement...
What type of substrate will you be installing flooring over? (concrete, wood, ?)
If you are removing the existing flooring materials to start from scratch from the existing subfloor, then you won't need to remove any baseboards. Just install your materials per manufacturer instructions while using the proper surface prep, tools, adhesives, etc.
Even if the material looks like it's super easy and simple to install ALWAYS go to the manufacturers own website and study the product files containing the surface prep required, installation method required, and any other information that you can track down prior to doing anything. There are typically lots of small details that are easy to overlook that can absolutely destroy your floor if you don't know about them. For instance, most manufacturers want you to leave a 1/4" - 1/2" expansion joint around the perimeter of the flooring to allow for seasonal expansion and contraction, etc. Most of them also say that if your subfloor dips or peaks more than 1/4" in a 10 foot span anywhere that you'll have to float/grind/fix it.
To make a long story short there is a lot of terrible misinformation out there and a general rule that you should always employ is to get your information from the source of the material. And when I say source I don't mean some hourly guy at a box store who maybe glanced at a flooring pamplet a few months ago, I'm referring to the manufacturer producing the material you want to install. They even have technical experts that you can call if you have any questions that aren't clearly answered in their product info files on their website. Don't hesitate to call them either, that's what they're there for.
As far as the order of installation you'd want to go, tile, floating hardwood, vinyl, and then carpet. The layout of your home might affect the last 3 slightly, but no matter what you'll want to get any tile done first.
As far as the floating hardwood in your kitchen are you referring to a laminate? Engineered hardwood? Or? They both have their ups and downs in a number of important catagories. Do you have pets? Kids?
If you have time to answer some or all of the above questions I could probably at least give you a rough idea of what might work better for you and why.. also, and this is probably the most important question, are you doing all of the installation? The proper installation of tile is actually quite involved, a LOT more involved than anything that is ever shown on HGTV, so if you decide to go that route then I can probably list out the majority of the steps that you would/should take to ensure a long lasting trouble free installation. I would never bid a job sight unseen, but most of what I would list out would be pretty general details regarding most installations.
Good luck with your project.