We have 3 dogs and 7 cats. Not one of the multiple combinations of relationships are the same. For example; the Maine Coone, Oskar, detests our one Lab. Has terrorized him since we got him. Alex, my Border Collie, he plays with nonstop and would never think of terrorizing. Our other Lab he ignores except for the occasional head rub. I could write an essay describing each relationship.
I will say that one should get a cat because they want a cat. They are not "simple" substitutes for dogs. They are very different creatures, but both species are domestic creatures and dependent on us for care. I would not trade my cats for anything, just like I would not trade my dogs for anything.
If you decide that a cat is what you want then I agree that a Maine Coone or a Siamese would give the best chance of success. Look for one who comes from a household with a dog.
Hope this helps.
Esox & Alex