Same here, I have a Linux Mint desktop set up for my kids and overall I'm happy with the performance. It hasn't been 100% smooth though. In particular updating from Mint 17 to Mint 18 took some effort to get things working properly. Maybe proprietary Nvidia drivers were to blame, but it didn't Just Work until I sat down with it and sorted things out.
Not that I'm saying that Debian is a better choice than Ubuntu here – Debian stable is Debian stable, and Ubuntu often contains stuff still considered experimental on Debian side – but unlike with, say, Fedora, many non-free drivers are included in the official repositories.
Would Debian be a smarter choice? Ubuntu's based on Debian GNU/Linux, and hardware support tends to come downstream from there. Steam based their OS on Debian, not Ubuntu. Do you know of any issues installing the .deb onto Debian?
Installing proprietary drivers is harder and pretty much all game devs test only with Ubuntu so you might get issues due to slightly different versions of some libraries.
Ubuntu is the distro everyone is targeting so for seamless experience you kinda need to stick with it.
Debian is ideologically opposed to things like closed source drivers that ubuntu makes easy. Not that there's anything wrong with that, it just makes it not a good choice for casual users and especially gamers.
I haven't tried installing it in Debian, I only have it installed as a GUI-less server, but in theory it should be fine.
The reason I mention Ubuntu is that the community is just much larger than that of Debian and there is more of a chance of someone already having solved any issues you may run into.
In my experience, steam works just fine under Debian. I previously ran it under Jessie with no problems, and currently run it under the pre-release version of Stretch also with no problems.
You can install Steam and NVIDIA proprietary drivers just fine on Arch Linux or any other distro, as well.
Ubuntu is the only officially supported distro, as in mentioned in system requirements, just because it's the most ubiquitous distro. It doesn't actually mean you will have any less problems with the problematic Linux games on Ubuntu, than on any other distro.
On Arch, with an NVIDIA card, getting this "all" up and running boils down to: sudo pacman -S steam nvidia
This gives you the most recent NVIDIA driver, 378.13-5.
