Let's assume you manage to set up your wireless network so you have decent connections. If you fail at that, your network is of no use to you anyway. I won't give you advice on setting up your wireless network — that's a question in its own right. The same goes for the question of what backup system to use.
So, with a good working wireless network, backing up a single laptop should work fine. There's no reason to suppose you'll have problems with your backup. The software that does the backup doesn't care what kind of network you have; the details are just beneath it's notice, down in the physical layer.
Assuming reliability, the only way your choice of networking technology can affect your backup is by slowing it down. But that's not going to happen. Even a cheap wireless router offers 300 Mbps (million bits per second), and a connection that fast is unlikely to be the slowest component in the connection between your laptop disk and the backup disk.
What will be? In your case, I'd look at that USB connection you plan to use to connect your backup drive. I don't know how common USB 3.0 is now, but it's the minimum you want for your purpose. Make sure both your router and your backup drive support it. The USB 2.0 interfaces that were standard the last time I bought a standalone drive max out at 1.5 Mbps for a sustained transfer, which can really slow you down.
Or you might consider buying a standalone device whose sole purpose is to provide a network drive. I use a cheap NAS (network attached storage) device that I bought a couple of years ago; it connects via Ethernet to my router, with an internal drive using a SATA interface (the same one your laptop uses). Lately, I've seen ads for "wifi drives" which act as a file service either directly or through a router, with no wiring required.
The last product should indicate to you how little you have to worry about wireless connections as part of your backup solution.