my preference is FreeBSD, but if you have ARM SBC like Raspberry Pi - you can use Linux with a last kernel compiled from source - NOT a dpkg/rpm/apt/yum provided one! If you can tell me more about the hardware setup you're using - I can be more specific in recommendations
UPDATE: As I see the hw specs - you will be perfectly fine with virtual machines! I do recommend VirtualBox - grab it and the extension pack. You'll need 2 VMs, one for Tor, one for a "browsing workstation". Tor one will be just fine on 1 CPU and 512Mb of ram, disk 4Gb will fit also, I do recommend Debian mini/netinstall - it is without graphics, and actually a bare OS - just what you need not to waste resources. Browsing VM can use 1 or 2 CPUs, 1Gb of ram - you can use the same iso but select the graphical desktop environment at the installation phase. The trick will be that desktop and the router will be in one virtual(not host-only!) network, so no data leaks will be there. Router will have 2 interfaces - one for a bridge to your actual network card that gives you the connection, it will be just like the one more PC in your network and your router will serve it all by itself just fine. On a desktop VM use Tor's SOCKS port and DNS port - and don't forget to fix the DNS server IP to your tor router VM. That's it!