You are on the right track.
Have a look at the Serial Input Basics tutorial, which shows you how to extract data surrounded by start and end markers, which in your example could be (if you take some care) '>' and '<'.
Obviously you will have to ignore irrelevant occurrences of those markers, so the solution will be highly specific to this type of message.
With Arduino it is best to avoid the problems caused by use of Strings and instead use the C-string processing functions in the <string.h> standard library.