I have Moon ones and can’t complain. I paid £25 for this set last year but there are better versions also. https://www.tredz.co.uk/.Moon-Meteor-X-Auto-Arctur-Light-Set_217880.htm
I always thought moon lights were good value and those ones have the daylight mode you would want for daytime visibility. I have a slightly older version without the daylight mode and it has been really good.
I recently bought some Exposure lights that have a 'daybright' function.
In terms of battery lights, I've found these Smart RL326R Trail 80 Lumens lights are super bright for daylight visibility:
I've still got one of their older 0.5w tail lights which has been excellent, but this one is even brighter.
On the front I've just bought a Sigma Sport Aura 45 USB front light with a shaped beam which meets German stzvo standards, so it actually does light up the road and not just dazzle oncomers. It also has an auto mode that adjusts brightness to ambient conditions: https://www.bikester.co.uk/sigma-sport-aura-45-usb-front-light-stvzo-1042199.html
But the best lights I've used are B&M dynamo lights, which come on automatically at night, and have an daytime visibility setting that really helps get you seen. I notice the difference in driver attitudes when I'm on one of my other bikes without them.
+1 for anything dynamo - lights on all the time and no fuss with batteries.
The moon nebula for a rear light is great - battery life is excellent, it has a day running mode, and can also be super bright if that's ever needed. The clamping mechanism also makes it really easy to take off quickly and fit any awkward shaped seat posts.
In terms of front lights, cateye lights are good quality but rather expensive if you want something that will light up the road.
EDIT: I think a pair of the nebulas will be perfect for what you need
FYI I bought this at the end. They are great!
Thanks everybody for the suggestions.
Any recommendations for front and rear lights? Looking something to improve chances to be seen during the day but also something decent for the sunset/night (in case of emergency). Thank you.