Before you worry too much about the product (laminate or vinyl), you will need to remove the tile WITHOUT disturbing the in-floor radiant heat. I'm going to guess the tile is sitting on radiant wires and not hydronic tubing. To jack out tiles without disturbing the wiring is SUPER DIFFICULT. I'm going to bet you will lose the radiant heat source simply by removing the tiles. Of course I'm only assuming you have radiant wires. Can you confirm what format of radiant heat you have?

The square edge is the issue...not the wood itself. The eased edge is what is going to save your tread/nosing. As soon as you get the rounded/eased edge you will STOP seeing this type of damage. Why? Because the edge is ALREADY ROUNDED. Right now you have a square edge that is being POUNDED into a 'rounded' edge. So you might as well beat it to the punch and round it off now....before there is MORE damage.

The flooring on the upper floor (aka bedrooms) can be different from the flooring in the main/public areas. I would pick a colour that is present in the Hickory wood sitting on your main floor and see if I could find a laminate that falls into that colour story. This will add continuity without competition (as little bug and Sina point out). Now the two issues you are about to face: the STAIRS (dun dun DUUUUUUN!!!) and the NOISE. Sigh. Carpets get rid of a tremendous amount of noise. Carpet keeps noise from escaping OUT of a bedroom as well as prevent it from ENTERING a bedroom. Here's what I suggest. Go ahead and rip out the carpet in the upstairs and then LIVE with noise/echo of the subfloor for a week. At that point you will either feel you have an INCREDIBLY well built house (unlikely but always a possibility) OR you will discover how LOUD everything/everybody really is (99% chance of this happening). And that's where you will start your 'carpet replacement' discussion. I have always said a cork floating floor (installed just like laminate) is a great carpet replacement. It is warm, soft and quiet. It deals with 80%-90% of the noise that carpet deals with. It is a 'like for like' replacement for carpet. Laminate is not. Laminate is a hard, rigid surface just like your subfloor (that you found to be quite loud). An acoustic underlayment can be used (QuietWalk Pro or 6mm cork underlay will do the trick) to keep noise transfer from "up down" noise. But it won't help with noise exiting the bedrooms, moving down the hallway and entering another bedroom. Only cork and carpet prevent that. Once you have chosen you material and the underlay thickness you can then tackle the stairs. This gets HORRIBLY tricky. I'm assuming the carpet is on the stairs as well? Right, now we have to keep the stairs to code so that the height of the rise is EQUAL all the way to the TOP FLOOR! That means you have to adapt all the tread/risers to match the FINAL height of the floor+underlayment. Zoinks. And I haven't even TOUCHED on the floor leveling needed once the carpet is removed. Carpets hide the WORST subfloors in the world. These subfloors are thin, wavy, pitched and are of low-grade materials (often fibre board sits on top...which does NOT like patching material). To get a rigid floor (floating or otherwise) you will need to level that subfloor. That's going to eat up $2-$4 per square foot ($2/sf is quite common...$4/sf is not likely but it has happened in REALLY sh!tty builds). And now that the subfloor has been leveled, you have to reassess the stairs. Or you can replace carpet with carpet. This may not be ideal if there are allergy suffers or asthmatics in the house...but it is always an option when replacing existing carpet.

Diagonal installs are done for two reasons: 1. A technical install...this means the subfloor is not thick enough AND the joists run in the wrong direction for the homeowner's tastes. A new home doesn't have either of these issues. 2. A HYPER modern look Remember: diagonal hardwood is a visual distraction that can cause some people to have balance issues in the rooms where the diagonal run occurs. I am one of those people. No matter how pretty it looks, I always end up slamming into walls, doorways and/or furniture because of the diagonal install. Just be very aware of what you are doing to yourself. Not many people know about the visual/balance issues. Not until they install it in their home and realize it was MASSIVE mistake.