Creating custom objects?

I believe you are on the right track, but I think what you are talking about is creating a database of cards that you can reference easily and change easily.

You could create a Serialized class and then create a MonoBehaviour with an array of that class made public. You could then simply just modify the GameObject from within Unity and add/remove cards as you need. If you wanted to get fancy, you could create an Editor class for Unity and have a decent interface for creating cards in your CardManager.

 using UnityEngine;
 using System.Collections;
 
 [Serializeable]
 public class Card
 {
    public String name = String.Empty;
    public Int32 damage = 0;
    public Int32 defense = 0;
 }

 public class CardManager : MonoBehaviour
 {
    public List<Card> cards = new List<Card>();
 
    public void Start()
    {
    }

    public void Update()
    {
    }
 }

I don't know why you think Card() should be a function. I also don't think you'd be creating new cards in the game, you'd have them all pre-designed.

So I would make each card a prefab, with a mesh and material for its appearance, and attach a "cardScript" on it that holds its stats.

 var theDeck : GameObject[];

 var myCards : List.<cardScript>();
 var yourCards : List.<cardScript>();

 function DealCards (howMany : int)
 {
 
 }

 function CompareCards (first : cardScript, second : cardScript)
 {
 
 }

There's a lot more to this sort of game that you're going to run into- how you are going to save a player's cards in a way that isn't easily cheatable, how to draw a random card with a the right probability based on its rarity, etc.