If you are a new member (no contracts before), there is a minimum buy-in.
If you are already an existing member, you can add on for as little as 25 points. For it to be considered an add-on, it has to be the same UY as your current contract (or one of your existing contracts) and in the exact same name.
The best thing to do would be to ask Disney. It used to be 160 but I have heard people say they bought in for less than that but I think that was at the worst of the recession. At the moment it is a very busy sales time so I'm not sure if Disney are in the mood to make it easier to buy in. Only Disney can really answer that question.
i would be sure to research resales before buying direct. remember that the rooms have been stayed in whether you buy direct or resale, so everyone is buying "used" in a sense. the few extra perks offered by buying direct have no real value - they just offer a few expensive alternative options to staying at DVC resorts.
also, there is no minimum when buying resale - i started with a 40 pt contract - but smaller contracts can be harder to find and tend to sell quickly.
there's a lot to know about DVC before buying in - make sure to take your time.
Current minimum is 100 points for a new purchaser at all existing resorts other than possibly AKV and Aulani. At those two, you must purchase at least 100 to get any discounts or incentives but DVD does not actually state one way or the other whether fewer points can be purchased by a new purchaser. Not sure you can still do just 50 (there was a designated 50 minimum for a while during the worst parts of the Great Recession).
If you are asking about Villas at Grand Floridian, DVD has not yet announced the minimum purchase for new purchasers.
I have never asked my guide but I have read over and over they will sell you 50 points - new member. I recently purchased 100 for my son but again, call Disney directly, rules/requirements can change on a daily basis.
I was offered 50 points as a new buyer. We ended up doing 70 because my kids are high school & college so we wanted enough for 4/5 nights in a studio spring break. We can relax in the sun or leisurely go to the parks.