There's been some great advice on here.
Good lights
Give yourself time.
I'd add to make sure you're comfortable being able to fix a puncture in the dark. That's where a detachable light can come in handy.
If I'm understanding correctly you're using Google to pick out a route? I wouldn't trust Google to take me across the road! I don't know how well you know the different road options, but I'd suggest trying
https://cycle.travel/ or even just taking some time to explore alternatives to the rough bits.
I don't want to put you off but rough and bad surfaces do not get better in foul weather
On the other hand, starting to commute was one of the best things I've done. An hour in the morning, arriving to work fresh and alert - best part of the day!
Take your time and it will all come good.
Best of luck!