Sorry about the inconvenience, obviously this should be much simpler.
– By proper I meant non-nightly. Both work fine but the nightly recently changed its repo which resulted in the first error message you posted. This is fixed now and both versions should install fine.
– The WiFi should work out of the box but the Pi’s antenna is not the greatest. Perhaps try connecting nearby your router for first setup. You can also try using WPS for connecting.
– There’s a difference between our beta image and our beta update. Beta version is based on Raspbian Stretch while beta update just adds our most recent bug fixes and changes which have not been officially released yet. However, LMS install should not even require a beta update at this point.
Please check your free space to rule it out as an error. You can see it in the Settings/Reboot Debug Info. You can also check the Health Checker there to make sure your Pi is running fine.