>>286131925L is the sweet spot for day hiking but too low for camping unless you go ultra minimal, which I would not recommend for a beginner. I'd get a separate pack for overnights though.
Appropriate shoes, clothes, first aid are most important. Also having enough water and bringing food you can enjoy while exercising. If you are alone, a garmin inreach or equivalent is nice but it'd singlehandedly blow through your budget. For me it was worth the peace of mind, I hike alone 99% of the time though. I only use it to have the SOS button.
>3-4 hour walks in the woodsThat's really all there is to hiking, there's nothing magical that happens when you hit hour 5. It's just walking. Of course trails can be easy or hard, well maintained or bushwacking, but for what youre doing it's little more than walks. Enjoy.