Should i use field.tpl.php or Display suite to add my own classes to fields?
It's matter of opinion, really. I'm using DS and it works fine, but it might have disadvantages later on, because I will have to export my settings to code with Features.

Also, DS isn't your only option - you can also try:


https://www.drupal.org/project/semantic_fields
https://www.drupal.org/project/field_formatter_class


and others. Which depends on your other needs - for example, are you planning to use DS multiple display modes handling?