First off - if I had to make a recommendation for any jam - it would have to be homemade. My mom's jams were always amazing.
With that said - if you are looking for an excellent storebought jam - I would highly recommend Bonne Maman - which is a Product of France. Specifically I would recommend their Blackberry Preserves. As I shop at Kroger stores I've noticed that they carry Bonne Maman jams in several different flavors (Strawberry, Raspberry, Blackberry, Mixed Berries, Blueberry, etc.). But invariably the Blackberry preservers are almost always sold out. So when I see some - along with their other jams - I make sure and grab a Blackberry.
They are usually about $6 dollars per 13 oz jar. So probably more expensive than other brands, but definitely better quality.
Here's their list of preserves: