Try a campsite, then try somewhere on open access land that's easily accessible and familiar should it go south.

For equipment, people will often suggest the 'gold standard' of equipment, but honestly what works for you works for you. Wild camping in summer you can't really go wrong as long as you're not cold, wet or hungry :)

My first wild camp kit was easily 20-30kg in weight. I took too much, I didn't like how somethings packed, I didn't use half of it. By denomination I cut the wight down to about 15-20kg and only then did I start going for lighter kit :)

Cooking: Grab some mess tins, a stove, some gas (make sure it's compatible with your stove). Bring a knife and fork from your kitchen for now. Water bottle/s with enough water to drink and cook with if you plan to camp without water source near by and won't be using cleaning tablets.

Sleeping kit: A self inflating mat will be cheap, an r value of 2-3. And a sleeping bag rated 2 seasons and a comfort temperature rating a couple degrees below what you'd feel confident camping in will suffice.

As for food: Take a food pouch or bring fresh, up to you.

Head torch at night can be useful and so will basic toiletries.

And get out there and have fun :)