Recommendations for best on the neck flea preventative for cats

My cats have not been outdoors for a year now, and I have found that one has flea bite dermatitis. The others are scratching too. I treated one room with fleabusters a year ago, but did not do the utility area, furnace room, and laundry room. Some eggs must have been dormant for a long time and then hatched, infecting the cats again. I am calling my vet tomorrow and having my husband pick up drops. Many people have strong feelings about the use of this product. I know it basically poisons the animals blood and the fleas then die after biting the animal. I don't want to use them, but have to do something. Which one is the best for cats? How long must I use them to break the cycle. I thought my flea problem was solved forever with the measures I took last year. Sadly, it's starting all over again. Thanks to anyone who can give me some pointers.