Wipe down your cat every other day with distilled water. This will neutralize the allergens in the fur.
Invest in a air purifier for your house/apartment.
Stick to one cat. Adding multiple cats will increase your chances of having an allergic reaction.
Try to avoid touching your eyes after petting your cat.
Some people say that long-haired cats cause fewer allergic reactions than short-haired cats as they don't shed the same. So try a Persian or Himalayan type.
Rex cats, which only have the undercoat, are less likely to trigger allergies, as they do not shed like ordinary cats.
People with cat allergies are often sensitive to the FelD1 protein present in cats. Many cats of the Siberian breed test very low in this protein and may be tolerated by some allergic people. This is a rare breed, but it is becoming more popular.
Beware of breeders claiming their cats are "hypo-allergic" - there is no such animal - all cats can trigger allergies, even the hairless kind. If you are allergic to saliva, then even the hairless kind will produce an allergic reaction as the cat does wash itself. In fact you might be more allergic (for that reason) to a hairless cat than to one that has fur!