Getters, setters, and properties best practices. Java vs. C#

I'm taking a C# class right now and I'm trying to find out the best way of doing things. I come from a Java background and so I'm only familiar with Java best-practices; I'm a C# novice!

In Java if I have a private property, I do this;

private String name;

public void setName(String name) {
   this.name = name;
}

public String getName() {
   return this.name;
}

In C#, I see that there are many ways of doing this.

I can do it like Java:

private string name;

public void setName(string name) {
   this.name = name;
}

public string getName() {
   return this.name;
}

Or I can do it this way:

private string name;

public string Name {
   get { return name; }
   set { name = value; }
}

Or:

public string Name { get; set; }

Which one should I use, and what are the caveats or subtleties involved with each approach? When creating classes, I am following general best-practices that I know from Java (especially reading Effective Java). So for example, I am favoring immutability (providing setters only when necessary). I'm just curious to see how these practices fit in with the various ways of providing setters and getters in C#; essentially, how would I translate best-practices from the Java world into C#?

EDIT

I was posting this as a comment to Jon Skeet's answer but then it got long:

What about a non-trivial property (i.e., with significant processing and validation perhaps)? Could I still expose it via a public property but with the logic encapsulated in get and set? Why would/should I do this over having dedicated setter and getter methods (with associated processing and validation logic).