1. Buy all the ownership and you have full control over your business.
2. Buy the business's stock, but you're either have less or no control over the business.
3. Buy a franchise and all you need is sell the product.
If you want to buy an existing business, the best is the first one, the safer is the second, and the third is depend on the business. Nowadays many project are making money by selling their franchise, so you need to beware about it.
I'd say buy all the ownership of existing business or start a new business are pretty much similar.
I agree with your list. Essentially, if op wants to buy without worrying about executive work then the third one is the best option. Franchising will keep you away from worrying about marketing and production. However, you need to make sure you have a good place for it where the product's target customers will be around. If op is a starting businessman without much background in business and only wants to gain quick profit then 2 and 3 are good options.