Run Steam in gamepadui/big-picture mode at boot

Pre config
You just need auto login an steam
 
Systemd-service
create sytemd service:
/etc/systemd/system/steam-bigpicture.service
[Unit]
Description=Steam Big Picture Mode
After=network.target
[Service]
User=YOUR_USER
ExecStart=/usr/bin/steam -gamepadui
Restart=on-failure
Environment=DISPLAY=:0
WorkingDirectory=/home/YOUR_USER
[Install]
WantedBy=graphical.target
Or as auto-run script
Create 
/etc/xdg/autostart/steam-big-picture.desktop
Or: 
~/.config/autostart/steam-big-picture.desktop
[Desktop Entry]
Type=Application
Exec=steam -gamepadui
Hidden=false
NoDisplay=false
X-GNOME-Autostart-enabled=true
Name=Steam Big Picture