Bushcraft is a good search term if you want to go as old school as possible. Ultralight is similar but using more modern equipment. Backpacking is the general term for long trips through the woods. Any of those will get you some good info on YouTube or various blogs to start with.
In warmer weather you can have a fine weekend with a very small amount of gear. A water filter, a dehydrated meal or two, and a small camp stove would be just fine for a beginner and shouldn’t cost too much for the basic version of any of them. Obviously many people would also want a tent and/or sleeping bag but you can decide how you want to handle that. Sleeping outside isn’t so bad and helps you appreciate a tent much more. Hammock camping is fairly popular as well so maybe consider that option if you want at least a bit of shelter without commiting to buying a tent right away.
I wouldn’t recommend foraging for food until you have some experience just being out there. Maybe bring a book about local plants on your first trip so that you can work on identifying them without the stress of them being your only food source.
The biggest piece of advice is just to get out there and see how it goes. Maybe you’ll love the freedom and challenge of having very little gear with you or maybe you’ll hate not having one specific comfort. Just pick a spot relatively close to civilization for your first trip so you can get out of any trouble you might find yourself in and you’ll be fine. Decide how you want the next trip to go based on the first one and just keep building from there.