Depends where the input is coming from.
If your input comes from the user, you should use the CultureInfo the user/page is using (Thread.CurrentThread.CurrentUICulture).
You can get and indication of the culture of the user, by looking at the HttpRequest.UserLanguages property. (Not correct 100%, but I've found it a very good first guess) With that information, you can set the Thread.CurrentThread.CurrentUICulture at the start of the page.
If your input comes from an internal source, you can use the InvariantCulture to parse the string.
The Parse method is somewhat easier to use, if your input is from a controlled source. That is, you have already validated the string. Parse throws a (slow) exception if its fails.
If the input is uncontrolled, (from the user, or other Internet source) the TryParse looks better to me.