There is a whole section on bike lights
https://www.bikeforums.net/electroni...hting-gadgets/ and at the top of the page you will find a lighting selection guide and separate listings for head and tail lights that are under $25.
You are going to get a lot of suggestions for common lights sold at your LBS or online. Many are pretty expensive and from my point of view are made with lots of useless bells and whistles. My own personal preference for a nightime headlight is a simple XML-T6 LED flashlight that can be powered by rechargeable 18650 batteries. The flashlight is less than $10 and the best NCR/Panasonic 3,400 mAh batteries cost around $7. It's focusable, can be aimed just where I want it, and when it runs low I can switch batteries in an instant. That's something very rare even in the more expensive bike lights.
The most recommended helmet light is the Lights and Motion helmet light. It's very effective but far too expensive at $130 for my tastes.
https://www.lightandmotion.com/shop/...ng/vis-360-pro
I have seen pcitures of a couple of DIY helmet lights made with much less expensive USB rechargeable lights. You probably don't need a 600 lumen helmet light. If a 100 lumen light works fine in the day, then it should be even better at night. Some of them look a little dorky but not all that much different than the Lights and motion light. Just search on DIY bike helmet light.