I have glass containers from IKEA for my fridge rather than plastic. I like that I can run them through the dishwasher (I’m mildly germophobic and irrational but it makes me feel better) and they can be used in the oven and microwave so they’re great for leftovers. They’re freezer safe too.
I realise this sounds daft but having specific places for each item in the fridge (and labelling them if necessary) helps to keep track. It can be easier to keep on top of organisation when it’s pretty.
I’ve trained all my family that things are used from the left/front and stacked from the right/back. That applies in the fridge, freezer and food cupboard.
Ideally do a fridge clear out before shopping, or at least as you put things away. Again I used to be reluctant to throw things away because I felt guilty about wasting food, but actually by being more ruthless I’ve learned to be more realistic about what I’m buying and cooking (I incorporate a soup/stir fry/omelette into the weeks meals)
Be realistic about leftovers and only keep what you’ll actually eat. I used to have a lot of guilt leftovers but I realised that it was better to put it straight in the bin and get better at judging portions/or find a nicer recipe than grow mould in the fridge!
I’ve found that leftovers can often be more useful frozen, when you pop them in the microwave for a quick meal at odd times, rather than in the fridge where you end up facing the same dinner again too soon.
I completely agree with keeping fruit/veg in view. It also helps to have at least a vague plan - I use up softer fruit, berries and veg at the start of the week and save the harder ones for the end of the week.
It’s taken me years to get the hang of this. I use my freezer a lot more which helps greatly in keeping the fridge under control.