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Check out this thread from 2013:

https://www.photoshopgurus.com/forum/photoshop-filters-plugins-and-effects/43550-adding-printed-effect-fonts.html

...especially posts #3 and #5.   It gives a simple way to sorta-kinda simulate the bumps and lumps on the edges of each character in conventional printing.

This "Sun" example you provided looks like it was done in the pre-Linotype period, maybe by a letterpress technique(?).  If so, the guy doing the compositing would occasionally / accidentally get one of the letters slightly out of alignment.  Also, the kerning of commercial printing in this period was primitive, at best.  Both of these features are easily simulated in PS or AI.

You may also be interested in how to physically distress (age) the labels you print on modern equipment to make them seem older:

http://www.instructables.com/id/Aged-Paper-Labels/step4/Aging-the-Paper/

http://www.instructables.com/id/Aged-Paper-Labels/step5/Distressing-the-Label/

http://www.instructables.com/id/Aged-Paper-Labels/step6/Burn-Marks/

http://www.instructables.com/id/Aged-Paper-Labels/step7/Sealing-and-Applying/

All of the above small factors, as well as choice of paper will contribute to an overall credibility of your effort.  It's up to you to decide on just how accurate do you want it to look.

HTH,

Tom M