What's your budget? You should read up on SmallNetBuilder articles to help tease out the BS of WiFi routers; if you're talking about the "2600Mbps" numbers, realize that's like a Formula 1 team saying, "We're not going to tell you the speed of
our car, but the total speed of all the cars on the racetrack combined...and these cars are using non-standard super tires that will destroy the track for everyone else and technically, we're going to get four cars and string them together to create little super units...even if that's not how the race runs and no car actually has the hardware to support linking up. That's...that's how we'll market it. Because that's what you wanted to know, right? Even though not a single car is actually going that speed. Because this number is bigger and people like bigger. I don't care if it's confusing or misleading. We're putting the combined number of every car, Dave, and that's that. And you know what? I'm going to take that number...and do the entire process at a totally different track and we're going to add those two total speeds together. Yes. This is it."
But the whole industry does that now, so nobody wants to fall behind with truthful numbers. But to figure out the actual speed of the single car (i.e., what speed your phone will connect at), it takes a bit of math.
Read this:
https://www.smallnetbuilder.com/basics/wireless-basics/32175-how-fast-can-your-wi-fi-go
Luckily, SNB tests just that: a single device connecting. The best way to analyze routers, IMO, is to look at their
real throughput over attenuation charts found here. Attenuation is loss/disruption of signal: distance = increases attenuation. walls/obstructions/metal walls = increase attenuation. interference (e.g., a microwave turning on) = increase attenuation. The best router will give higher throughput (measured in Mbps) at higher attenuation (measured in dB). Right? Even with a lot of walls and obstruction (i.e., high attenuation), you'd want higher throughput. You can see the average, or just pick a high attenuation to see the details. You'll see many of them drop under 100Mbps (especially on 2.4GHz).
For speed alone (forgetting all other performance features like beamforming, MU-MIMO, etc.), look at higher thoroughput at a high attenuation.
https://www.smallnetbuilder.com/tools/charts/router/view
Right, there's two WiFi frequencies these days: 2.4GHz and 5GHz. The 5GHz is faster, but longer range; 2.4GHz is slower, but higher range. 5GHz is optional; not all devices support it, so even if your router has it, it won't do any good. But
most newer devices come with both 2.4GHz and 5GHz (also known as bands; so dual-band means you have both frequencies).
Notice that attenuation can bring some routers down to lower speeds. But if they're still faster than your internet, then you're golden. The only time you'd sincerely want higher throughput than your internet is for large transfers
within your network (not going to the internet at all; just between devices on your network). This is either for NAS or local media streaming.
Briefly, for 3 floors, you'd want to place the router in the central location on the 2nd floor (central being the center spot of all the places you'd be using WiFi; if you only use WiFi on the left side of the house, then, put the router closer to
that "center").
EDIT: for your recommendation, right. I'm not sure which two those first routers are, but check the charts. See which has higher throughput at higher attenuation.
That one will give you the best speeds with the most obstacles in the way (like your three floors). If you're just looking for maximum speed right next to the router, just use 3 or 6dB attenuation and see the fastest one that'll fit in your budget.