First, let's be clear: 'Keyboard' is a different skill from 'piano.' The keys may look the same, but the technique you develop for playing them is quite different. So don't get confused about what you are doing.
Either way, 61 keys is enough to get started, but a keyboard you can get for under $100 will be lacking in many other amenities needed to make the experience *musical.* It's like trying to learn to ride a horse by practicing on a goat. Hey, they both have 4 legs, don't they?
I would venture to predict that, if you do have any serious musical talent, you will run out patience with your toy (i.e. <$100) keyboard in just a few weeks, if not days. Then you'll want the $400-500 keyboard, which could last you maybe a year or two, depending on your taste in music. Then you'll be ready for a real instrument