How can I interpret "typical both of a particular class"?

Solution 1:

Whatever the link you make between typical and particular, you do not need to be worried that they clash in your sentence. particular simply modifies one of the categories "we were typical of". You can simplify and say:

We were, I think, typical both of A and, by contrast, of B.

where A is

a particular (certain, specific) class of pre-war Germans

We were representative of a particular class, not of any class.

Solution 2:

Typical means

having the distinctive qualities of a particular type of person or thing.

You have a certain class of pre-war Germans consisting of a group of people with certain characteristic. The writer is a typical example of those people, as well as the postwar country at large.