I’m working on a binary tree implementation in Java and need to ensure it performs optimally for both insertions and lookups. Currently, the implementation is a basic binary search tree (BST) and does not guarantee balanced insertions, which can lead to degraded performance in the worst case.

public class BinaryTree {
private Node root;

private static class Node {
    int value;
    Node left, right;

    Node(int value) {
        this.value = value;
        this.left = null;
        this.right = null;
    }
}

public void insert(int value) {
    root = insertRec(root, value);
}

private Node insertRec(Node root, int value) {
    if (root == null) {
        root = new Node(value);
        return root;
    }

    if (value < root.value) {
        root.left = insertRec(root.left, value);
    } else if (value > root.value) {
        root.right = insertRec(root.right, value);
    }
    return root;
}

public boolean search(int value) {
    return searchRec(root, value) != null;
}

private Node searchRec(Node root, int value) {
    if (root == null || root.value == value) {
        return root;
    }

    if (value < root.value) {
        return searchRec(root.left, value);
    }
    return searchRec(root.right, value);
}

public void inorder() {
    inorderRec(root);
}

private void inorderRec(Node root) {
    if (root != null) {
        inorderRec(root.left);
        System.out.print(root.value + " ");
        inorderRec(root.right);
    }
}

1. How can I modify the BinaryTree implementation to ensure that the tree remains balanced, thus improving performance for both insertion and lookup operations?
2. What are the trade-offs between different types of balanced trees, such as AVL trees and Red-Black trees, in terms of complexity and performance?
3. How can I implement these balanced tree structures, and what are the key considerations for maintaining balance during insertions and deletions?