How to handle shared_ptr (or other smart ptr) members in constructors and assignment operators?

I'm trying to implement a linked list with smart pointers, to get used to using them. However I really can't wrap my head around how to handle them in constructors and assignment operators, I get lots of weird errors and I don't even know how to google them, so I thought asking here would be the simplest.

Here is my generic Link class in its current form, how it seems logical to me. The default constructor does not work, and I don't understand why. Can you show me whats the correct and elegant way to make a class that uses shared pointers?

template<class T>
class Link {
public:
    template<typename> friend class LinkedList;

    Link() :next(make_shared<Link<T>>), prev(make_shared<Link<T>>), val(0) {}
    Link(const T& data) :next(make_shared<Link<T>>), prev(make_shared<Link<T>>), T(data) {}
    Link(const Link<T>& other) :val(other.val),
         next(make_shared<Link<T>>(other.next)),
         prev(make_shared<Link<T>>(other.prev)) {}
    Link(Link<T>&& other) :val(move(other.val)),
         next(move(other.next)),
         prev(move(other.prev)) {}


    Link<T>& operator=(const Link<T>& other) {
        val = other.val;
        next = other.next;
        prev = other.prev;
        return *this;
    }

    Link<T>& operator=(Link<T>&& other) {
        next = make_shared<Link<T>>(std::move(other.next));
        prev = make_shared<Link<T>>(std::move(other.prev));
        val = std::move(other.val);
        return *this;
    }

    ~Link() {
        cout << val << "   destroyed" << endl;
    };
private:
    shared_ptr<Link<T>> next;
    shared_ptr<Link<T>> prev;
    T val;
};