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It's difficult to make recommendations without knowing your tastes. My mum loves Camembert and smelly Brie, but hates anything blue. I love blue cheese with Port. DD loves cheddars and I find them either too boring or mouth-stingingly strong.
The best thing to do is go to the cheese counter and try a few. Waitrose usually have a good selection in. Good cheese can also be eye-wateringly expensive.
Serve cheese at room temperature, not straight from the fridge. If it stays cold then you can store it outside if it's a bit stinky. Ensure it's well covered and secure from cats and rats though.