I am running Ubuntu 18.04 on my Microsoft Surface Pro 3, and in general it works really well.
I have had problems with the wifi going down, which seems to be related to power changes. Following the instructions given in this Reddit thread I edited the file /etc/NetworkManager/conf.d/default-wifi-powersave-on.conf and set the value wifi.powersave = 2.
There is some useful information for setting up Linux on the Surface Go here.
To get the best out of the battery, I recommend building and running powertop. Boot up your surface, so all the kernel settings are set to their defaults, and then run ‘sudo powertop –html’. This will create an HTML file in the current directory named “powertop.html”. Open it with an editor and do a search for all the ‘echo’ command line statements. These are the proc settings to optimise your power. You can copy these commands to a shell script that can either be run manually or on boot.
This is what is in my shell script:
echo '1500' > '/proc/sys/vm/dirty_writeback_centisecs'
echo '0' > '/proc/sys/kernel/nmi_watchdog'
echo '1' > '/sys/module/snd_hda_intel/parameters/power_save'
echo 'min_power' > '/sys/class/scsi_host/host0/link_power_management_policy'
echo 'min_power' > '/sys/class/scsi_host/host1/link_power_management_policy'
echo 'min_power' > '/sys/class/scsi_host/host2/link_power_management_policy'
echo 'auto' > '/sys/bus/i2c/devices/i2c-5/device/power/control'
echo 'auto' > '/sys/bus/i2c/devices/i2c-7/device/power/control'
echo 'auto' > '/sys/bus/i2c/devices/i2c-2/device/power/control'
echo 'auto' > '/sys/bus/i2c/devices/i2c-3/device/power/control'
echo 'auto' > '/sys/bus/i2c/devices/i2c-4/device/power/control'
#echo 'auto' > '/sys/bus/usb/devices/1-6/power/control'
#echo 'auto' > '/sys/bus/usb/devices/1-1.4/power/control'
#echo 'auto' > '/sys/bus/usb/devices/1-1.3/power/control'
echo 'auto' > '/sys/bus/i2c/devices/i2c-6/device/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:14.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:03.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:02.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:00.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:1b.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:01:00.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:16.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:1f.0/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:1f.2/power/control'
echo 'auto' > '/sys/bus/pci/devices/0000:00:1f.3/power/control'
(Note that I have commented out a couple of lines that change the power settings on some USB controllers. I found that they caused problems with my external keyboard and mouse)