When to save postmarks or not?

Every collector will have differing opinion.
It will be up to the individual.

My Hierachy
Mint stamp
cover Indicia
slogan
(decent) Postmark
Used stamp

Using you image for example
I'd keep the slogans (Just one of the West Point)
Soak the US footprint pmks

Soaking ONLY the stamps that are to go to an album
Only clear readable postmarks on modern mail
Save Postmarks on very early stamps
These can be valuable
But only time will make you feel comfortable
on what you have the space to collect and the time.

Try to adopt a feeling that you are a caretaker of Philatelic material.

Australian Postmark  values (minimum of $4 a stamp)


Don't be afraid to collect the ripped and torn

Postmarks are collectable for their interest beyond the stamp itself, and sometimes the postmark value is much more than the stamp


You would be advised to keep if
1. they are clearly readable .especially  "Socked on the nose" 
2. come from small obscure or unusual post offices (many long closed down for economy) some of these are Rare RRR 
3. Have an interesting date of use , eg  First day of use  
4.  are accompanied by  a complete  illustration or a slogan 
5. Older stamps often had a killer cancel with a number assigned to the town  so numeral postmarks are a whole collecting field , Similarly with US  "Fancy Cancels" again sometimes   rare 

Common cancels from major towns and Cities generally have little interest and can be safely soaked  

57buick , the decision regarding what is collectable is defined by you. The examples in your photograph are clearly the remnants of someone else's decision about what they considered collectable. The study and collection of postmarks, cancellations and postal markings, marcophily or marcophilately, is a field of philately in and of itself, and as such every postmark is potentially of value.

As there is only so much space, money and effort that you can pour into this, I recommend saving / collecting what interests you and build on that. This could be postmarks linked to a single place, era or theme. Your photograph shows that the previous owner cut out his postmarks in the classic collecting style of 2x4-inch cutouts. Collecting today, I recommend keeping the entire cover as the cutouts remove crucial information, such as where the cover was sent and how it was handled. In larger post offices with multiple machines, this extra information could identify machines used only for local or international mail, or which handled 'other' items (such as mail that wouldn't fit in the conventional machines, or which may have had a stamp applied in a non-conventional location).

Generally, albums are not great storage options in this field, especially if you start collecting large numbers (I have thousands). I prefer keeping my collection in small boxes (shoe boxes are great). As some of the previous replies show, there are catalogues for postmarks. Reading these for the areas that interest you can give you a huge headstart on what to look out for, to recognise the rare and unusual! They can be expensive, so start by ordering from the library. I grab catalogues and monographs on my interest area from auctions when they come available.

 I would keep all of those posted, if the postmark is clear I won't soak anything. A dedicated album will give you pleasure in the future.

Cancellations are a postal imprint that will not recur the next day.  Save them.