I use up whatever is oldest first, not in terms of date necessarily, but in terms of colour and texture. If plans change and there will be too much left from the shopping I will freeze it.
I don't do meal plans, I buy the right amount for the week from what is available when I am in the shop, and work through it as above.
I buy chopped garlic in jars. Keep veg in the fridge rather than a rack as it stops it going wrinkly, not potatoes though, they are kept in a potato store basket. Carrots, parsnips etc. I leave on the side to dry off because they are always moist from the change of temperature, then wrap in foil, ensure it is airtight and keep in the fridge. Onions in a bowl with foil loosely laid on top. Cool and dark corner of the kitchen. Same with lemons and apples.
I don't buy bagged salad or leaves, it is never finished and goes slimy quickly, I have never managed to use an entire bag.
Make sauces with older stuff. I buy dried and tinned food so less fresh to go off. Lots of lentils, they keep a long time, chickpeas, although dry are no good when they get too old.
I cook by using what needs using and freezing spare meals or using it the next day, saves waste and time.