@juliediane 

You are asking a couple of questions, so I'll cover them individually.

Arris TM1602

I had one of them and couldn't wait to get rid of it. It is a good modem, just that it is DOCSIS 3.0, and it has the PUMA 6 chipset  I can't post an non-TP-Link here so Google "Intel Puma 6 Modem List Chipset Defects" and from it:

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Intel’s Puma 6 chipset included in several cable modems is defective as it allows high spikes in network latency quite often (slow web page loading, for example). These severe network latency spikes interfere with online gaming, streaming video, or simply surfing the web. Network jitter (variable latency) also causes problems.

The Puma 6 modems suffer from both latency and jitter. Some firmware updates have only temporarily fixed the problem and it seems Intel has no real fix for the issue. Consequently, these bad internet connections landed cable modem maker ARRIS in trouble with a pending lawsuit filed in California.

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There is a TM1602A that may not have this problem.

The modem is capable of 600Mbps down though, but the ISP can control that by the number of channels it uses to be less.

For the future, you DO want a DOCSIS 3.1 modem. Just Google "docsis 3.0 vs 3.1" to see more.

Ubee

I have Spectrum and when they went from 200Mbps to 400Mbps they replaced my TM1602 with a Ubee e31u2v1, which is just a Voice Modem. The do have a Ubee Modem/Router too but since I had my own router that gave me that one. Even if I got the Modem/Router, they could turn-off the WiFi and Bridge the Modem/Router to be Modem only. I am very happy with the Ubee...Check with yout ISP and see what they can provide in a Voice Modem only for you, might be the same one I have.

New Router

Well, I suspect your problem is the floors, not the size of the home. Floors can tough to get through for WiFi. I've got a single story home a little larger with no problems with my older Archer A20 and now an AX55 (upgraded to AX speed from AC). You may need a MESH system to cover the home. See https://www.tp-link.com/us/mesh-wifi/ for more info. I'd also plan for the future, higher speeds will come sooner than one things, and new devices will probably be AX speed now. An X55 should suite you fine. I Beta tested this (https://www.tp-link.com/us/deco-mesh-wifi/product-family/deco-x55/) and it worked well for me too. Had the master next to the modem at one end of the house, our masster bedroom is at the other end of the house, maybe 60 feet away and place the secondary node just outside the bedroom door. Extended the range outside the house as well. Great product. It does come in a 2 or 3 pack unit, you might need the 3 pack, on unit on each floor for best coverage.