Which Linux is smaller and softer :)?

Question

linux

I ask you to help with the choice of Linux, because. I didn’t work with it very much myself and I don’t have experience in this :(
Linux is planned to be launched from under VirtualBox, despite the fact that 2 network cards will be forwarded into it, the first will be with Wifi cards, the second is a Virtual Host Adapter. The bottom line is that in Linux "share" the Internet of the first port to the second.
Why is it necessary? To turn a "non-cashier" wifi usb adapter into a "cashier" cable ethernet adapter, which the software on the Host machine should eat with pleasure :) He got poisoned from the Wifi adapter and now feels bad :)
_ the machine is weak, Linux is needed, which works well with virtualbox network adapters, which consumes little RAM and CPU.

Answer 1

dd-wrt or pfsense might be your best bet.
and there are many more solutions.

Answer 2

Arch - Stylish × Fashionable × Youthful

Answer 3

minimal images of ubuntu and centos run on a machine with 256 MB of memory and work for me as routers and vpn servers.

Answer 4

For Docker, the minimum debian image is ~100MB, ubuntu and centos are twice as thick. If only the kernel and basic services are running - it will survive on 32MB, although more may be needed for installation.
Z.Y. Wangyu problems with the work of the WiFi card, forwarded to VirtualBox via USB.