Cheddar is great with everything. I personally like it mild or medium.
I'd have to say my favourite is Mozzarella followed very closely by Halloum cheese. It's a pretty tough call between the two actually.
Cream cheese is pretty good, does it count as cheese?
Next I'd say Swiss cheese just coz it's pretty versatile as well.
After those comes Kashkaval and various other metly cheeses.
Feta, White.. All good too.
I generally like stuff that doesn't have a strong, almost offensive flavour. The only one I'd really consider is Gorgonzola, mainly in sauces.