I probably land around 75% generic/25% branded.
The first basket tends to be things like staples (flour/sugar/cooking oil), sandwich bread, dairy products (milk, butter, eggs, etc.) Ditto for some household supplies (I typically buy the store brand version of Bounty and Charmin for paper towels and toilet paper, etc.) as well as OTC medicine.
The second basket is mostly things like snack foods and soft drinks (pop/soda) - if I’m going to have food like Oreos, Coke, or Doritos, I don’t want a poor substitute, plus these are things I’ve noticed are substantially different. I also splurge on some nicer cheeses and lunch meat. I also tend to buy personal care products from major brands (Dove or Dial soap, Colgate toothpaste, etc.)
For me, it’s not about being “cheap” or chasing the lowest price possible - it’s more about getting a good value. I have no issue paying more for branded products if I feel that they are better/more enjoyable in an appreciable way. Things like store brand butter and cooking oil are an easy way to save a buck while shopping, which I care about since that’s a dollar I can do or buy something more enjoyable with.
A lot of things that are available brand name are really just commodities. I have one heck of a time finding any qualitative difference between sliced white bread of any brand. It's intentionally bland and hard to get wrong when made at an industrial scale with any competent production. But then there's specialty products where I can easily tell the difference between things like artisan bread that's made by hand.
Things made with proprietary recipes like Oreos are clearly going to be different.